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Parshat Kedoshim and the Ten Commandments
In the first four psukim of Parshat Kedoshim, the parallels to some of the 'dibrot' [the Ten Commandments] are rather obvious [e.g. honoring one's parents, keeping Shabbat, idol worship etc.]. However, as the Parsha continues, the parallels become less obvious, and as we will see, some of the parallels to the dibrot become rather 'stretched' and others appear to be missing!
Nonetheless, it would be logical to assume that there must be a deeper reason for these parallels, and the manner of their presentation.
Let's begin by taking note of an interesting internal pattern within Parshat Kedoshim, that may help us 'crack the code'.
In the first 18 verses of Parshat Kedoshim, the 'refrain' ANI HASHEM is repeated EIGHT TIMES (at the end of just about every other pasuk). Note as well how this refrain appears in two different forms:
ANI HASHEM ELOKEICHEM - the first four (see 19:1-10);
ANI HASHEM - the next four times (see 19:11-18).
Many commentators over the centuries have grouped the Ten Commandments into two groups, and each group uses one of these two refrains.
  1. Mitzvot ben Adam La-Makom / Commandments between people and God (like rituals and such) - Ani Hashem Eloheichem
  2. Mitzvot ben Adam Le-chavero / Commandments between people (how we treat each other) - Ani Hashem
The Ten Commandments (Mount Sinai / Exodus)
(א) וַיְדַבֵּ֣ר אֱלֹקִ֔ים אֵ֛ת כׇּל־הַדְּבָרִ֥ים הָאֵ֖לֶּה לֵאמֹֽר׃ {ס}

(1) God spoke all these words, saying:

I. Between people and God

(ב) אָֽנֹכִ֖י֙ ה' אֱלֹקֶ֑֔יךָ אֲשֶׁ֧ר הוֹצֵאתִ֛יךָ מֵאֶ֥רֶץ מִצְרַ֖יִם מִבֵּ֣֥ית עֲבָדִ֑͏ֽים׃

(2) I ה' am your God who brought you out of the land of Egypt, the house of bondage:

(ב) דַּבֵּ֞ר אֶל־כׇּל־עֲדַ֧ת בְּנֵי־יִשְׂרָאֵ֛ל וְאָמַרְתָּ֥ אֲלֵהֶ֖ם קְדֹשִׁ֣ים תִּהְי֑וּ כִּ֣י קָד֔וֹשׁ אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(2) Speak to the whole Israelite community and say to them: You shall be holy, for I, your God ה', am holy.

II. Between people and God
(ג) לֹֽ֣א־יִהְיֶ֥͏ֽה־לְךָ֛֩ אֱלֹקִ֥֨ים אֲחֵרִ֖֜ים עַל־פָּנָֽ͏ַ֗י׃ (ד) לֹֽ֣א־תַֽעֲשֶׂ֨ה־לְךָ֥֣ פֶ֣֙סֶל֙ ׀ וְכׇל־תְּמוּנָ֔֡ה אֲשֶׁ֤֣ר בַּשָּׁמַ֣֙יִם֙ ׀ מִמַּ֔֡עַל וַֽאֲשֶׁ֥ר֩ בָּאָ֖֨רֶץ מִתָּ֑͏ַ֜חַת וַאֲשֶׁ֥ר בַּמַּ֖֣יִם ׀ מִתַּ֥֣חַת לָאָֽ֗רֶץ׃ (ה) לֹֽא־תִשְׁתַּחֲוֶ֥֣ה לָהֶ֖ם֮ וְלֹ֣א תׇעׇבְדֵ֑ם֒ כִּ֣י אָֽנֹכִ֞י ה' אֱלֹקֶ֙יךָ֙ אֵ֣ל קַנָּ֔א פֹּ֠קֵד עֲוֺ֨ן אָבֹ֧ת עַל־בָּנִ֛ים עַל־שִׁלֵּשִׁ֥ים וְעַל־רִבֵּעִ֖ים לְשֹׂנְאָֽ֑י׃ (ו) וְעֹ֥֤שֶׂה חֶ֖֙סֶד֙ לַאֲלָפִ֑֔ים לְאֹהֲבַ֖י וּלְשֹׁמְרֵ֥י מִצְוֺתָֽי׃ {ס}

(3) You shall have no other gods besides Me. (4) You shall not make for yourself a sculptured image, or any likeness of what is in the heavens above, or on the earth below, or in the waters under the earth. (5) You shall not bow down to them or serve them. For I your God ה' am an impassioned God, visiting the guilt of the parents upon the children, upon the third and upon the fourth generations of those who reject Me, (6) but showing kindness to the thousandth generation of those who love Me and keep My commandments.

(ד) אַל־תִּפְנוּ֙ אֶל־הָ֣אֱלִילִ֔ם וֵֽאלֹקֵי֙ מַסֵּכָ֔ה לֹ֥א תַעֲשׂ֖וּ לָכֶ֑ם אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(4) Do not turn to idols or make molten gods for yourselves: I ה' am your God.

III. Between people and God
(ז) לֹ֥א תִשָּׂ֛א אֶת־שֵֽׁם־ה' אֱלֹקֶ֖יךָ לַשָּׁ֑וְא כִּ֣י לֹ֤א יְנַקֶּה֙ ה' אֵ֛ת אֲשֶׁר־יִשָּׂ֥א אֶת־שְׁמ֖וֹ לַשָּֽׁוְא׃ {פ}

(7) You shall not swear falsely by the name of your God ה'; for ה' will not clear one who swears falsely by God’s name.

No apparent parallel to Parshat Kedoshim.
Hmmmm...
We will return to this question in a bit.
IV: Between people and God
(ח) זָכ֛וֹר֩ אֶת־י֥֨וֹם הַשַּׁבָּ֖֜ת לְקַדְּשֽׁ֗וֹ׃ (ט) שֵׁ֤֣שֶׁת יָמִ֣ים֙ תַּֽעֲבֹ֔ד֮ וְעָשִׂ֖֣יתָ כׇּֿל־מְלַאכְתֶּֽךָ֒׃ (י) וְי֨וֹם֙ הַשְּׁבִיעִ֔֜י שַׁבָּ֖֣ת ׀ לַה' אֱלֹקֶ֑֗יךָ לֹֽ֣א־תַעֲשֶׂ֣֨ה כׇל־מְלָאכָ֜֡ה אַתָּ֣ה ׀ וּבִנְךָ֣͏ֽ־וּ֠בִתֶּ֗ךָ עַבְדְּךָ֤֨ וַאֲמָֽתְךָ֜֙ וּבְהֶמְתֶּ֔֗ךָ וְגֵרְךָ֖֙ אֲשֶׁ֥֣ר בִּשְׁעָרֶֽ֔יךָ׃ (יא) כִּ֣י שֵֽׁשֶׁת־יָמִים֩ עָשָׂ֨ה ה' אֶת־הַשָּׁמַ֣יִם וְאֶת־הָאָ֗רֶץ אֶת־הַיָּם֙ וְאֶת־כׇּל־אֲשֶׁר־בָּ֔ם וַיָּ֖נַח בַּיּ֣וֹם הַשְּׁבִיעִ֑י עַל־כֵּ֗ן בֵּרַ֧ךְ ה' אֶת־י֥וֹם הַשַּׁבָּ֖ת וַֽיְקַדְּשֵֽׁהוּ׃ {ס}

(8) Remember the sabbath day and keep it holy. (9) Six days you shall labor and do all your work, (10) but the seventh day is a sabbath of your God ה': you shall not do any work—you, your son or daughter, your male or female slave, or your cattle, or the stranger who is within your settlements. (11) For in six days ה' made heaven and earth and sea—and all that is in them—and then rested on the seventh day; therefore ה' blessed the sabbath day and hallowed it.

(ג) אִ֣ישׁ אִמּ֤וֹ וְאָבִיו֙ תִּירָ֔אוּ וְאֶת־שַׁבְּתֹתַ֖י תִּשְׁמֹ֑רוּ אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(3) You shall each revere your mother and your father, and keep My sabbaths: I ה' am your God.

V: Between people and God / Between people and people
(יב) כַּבֵּ֥ד אֶת־אָבִ֖יךָ וְאֶת־אִמֶּ֑ךָ לְמַ֙עַן֙ יַאֲרִכ֣וּן יָמֶ֔יךָ עַ֚ל הָאֲדָמָ֔ה אֲשֶׁר־ה' אֱלֹקֶ֖יךָ נֹתֵ֥ן לָֽךְ׃ {ס}

(12) Honor your father and your mother, that you may long endure on the land that your God ה' is assigning to you.

(ג) אִ֣ישׁ אִמּ֤וֹ וְאָבִיו֙ תִּירָ֔אוּ וְאֶת־שַׁבְּתֹתַ֖י תִּשְׁמֹ֑רוּ אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(3) You shall each revere your mother and your father, and keep My sabbaths: I ה' am your God.

Note, however, that we have two problems.
First of all, we did not find any obvious parallel for the third Commandment.
But we also did not find any parallel for the laws discussed in 19:5-10 [i.e. the laws of 'pigul' and 'pe'a' etc.].

(ה) וְכִ֧י תִזְבְּח֛וּ זֶ֥בַח שְׁלָמִ֖ים לַה' לִֽרְצֹנְכֶ֖ם תִּזְבָּחֻֽהוּ׃ (ו) בְּי֧וֹם זִבְחֲכֶ֛ם יֵאָכֵ֖ל וּמִֽמׇּחֳרָ֑ת וְהַנּוֹתָר֙ עַד־י֣וֹם הַשְּׁלִישִׁ֔י בָּאֵ֖שׁ יִשָּׂרֵֽף׃ (ז) וְאִ֛ם הֵאָכֹ֥ל יֵאָכֵ֖ל בַּיּ֣וֹם הַשְּׁלִישִׁ֑י פִּגּ֥וּל ה֖וּא לֹ֥א יֵרָצֶֽה׃ (ח) וְאֹֽכְלָיו֙ עֲוֺנ֣וֹ יִשָּׂ֔א כִּֽי־אֶת־קֹ֥דֶשׁ ה' חִלֵּ֑ל וְנִכְרְתָ֛ה הַנֶּ֥פֶשׁ הַהִ֖וא מֵעַמֶּֽיהָ׃

(ט) וּֽבְקֻצְרְכֶם֙ אֶת־קְצִ֣יר אַרְצְכֶ֔ם לֹ֧א תְכַלֶּ֛ה פְּאַ֥ת שָׂדְךָ֖ לִקְצֹ֑ר וְלֶ֥קֶט קְצִֽירְךָ֖ לֹ֥א תְלַקֵּֽט׃ (י) וְכַרְמְךָ֙ לֹ֣א תְעוֹלֵ֔ל וּפֶ֥רֶט כַּרְמְךָ֖ לֹ֣א תְלַקֵּ֑ט לֶֽעָנִ֤י וְלַגֵּר֙ תַּעֲזֹ֣ב אֹתָ֔ם אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(5) When you sacrifice an offering of well-being to ה', sacrifice it so that it may be accepted on your behalf. (6) It shall be eaten on the day you sacrifice it, or on the day following; but what is left by the third day must be consumed in fire. (7) If it should be eaten on the third day, it is an offensive thing, it will not be acceptable. (8) And one who eats of it shall bear the guilt for having profaned what is sacred to ה'; that person shall be cut off from kin.

(9) When you reap the harvest of your land, you shall not reap all the way to the edges of your field, or gather the gleanings of your harvest. (10) You shall not pick your vineyard bare, or gather the fallen fruit of your vineyard; you shall leave them for the poor and the stranger: I ה' am your God.

Before we return to this question, let's take a look at the second group:
VI-IX: Between people and people

(יג) לֹ֥֖א תִּֿרְצָ֖͏ֽח׃ {ס}

לֹ֣֖א תִּֿנְאָ֑͏ֽף׃ {ס}

לֹ֣֖א תִּֿגְנֹֽ֔ב׃ {ס}

לֹֽא־תַעֲנֶ֥ה בְרֵעֲךָ֖ עֵ֥ד שָֽׁקֶר׃ {ס}

(13) You shall not murder.

You shall not commit adultery.

You shall not steal.

You shall not bear false witness against your neighbor.

(טז) לֹא־תֵלֵ֤ךְ רָכִיל֙ בְּעַמֶּ֔יךָ לֹ֥א תַעֲמֹ֖ד עַל־דַּ֣ם רֵעֶ֑ךָ אֲנִ֖י ה'׃

(16) Do not deal basely with members of your people. Do not profit by the blood of your fellow [Israelite]: I am ה'.

(כ) וְ֠אִ֠ישׁ כִּֽי־יִשְׁכַּ֨ב אֶת־אִשָּׁ֜ה שִׁכְבַת־זֶ֗רַע וְהִ֤וא שִׁפְחָה֙ נֶחֱרֶ֣פֶת לְאִ֔ישׁ וְהׇפְדֵּה֙ לֹ֣א נִפְדָּ֔תָה א֥וֹ חֻפְשָׁ֖הֿ לֹ֣א נִתַּן־לָ֑הּ בִּקֹּ֧רֶת תִּהְיֶ֛ה לֹ֥א יוּמְת֖וּ כִּי־לֹ֥א חֻפָּֽשָׁה׃ (כא) וְהֵבִ֤יא אֶת־אֲשָׁמוֹ֙ לַֽה' אֶל־פֶּ֖תַח אֹ֣הֶל מוֹעֵ֑ד אֵ֖יל אָשָֽׁם׃ (כב) וְכִפֶּר֩ עָלָ֨יו הַכֹּהֵ֜ן בְּאֵ֤יל הָֽאָשָׁם֙ לִפְנֵ֣י ה' עַל־חַטָּאת֖וֹ אֲשֶׁ֣ר חָטָ֑א וְנִסְלַ֣ח ל֔וֹ מֵחַטָּאת֖וֹ אֲשֶׁ֥ר חָטָֽא׃ {פ}
(20) If a man has carnal relations with a woman who is a slave and has been designated for another man, but has not been redeemed or given her freedom, there shall be an indemnity; they shall not, however, be put to death, since she has not been freed. (21) But he must bring to the entrance of the Tent of Meeting, as his guilt offering to ה', a ram of guilt offering. (22) With the ram of guilt offering the priest shall make expiation for him before ה' for the sin that he committed; and the sin that he committed will be forgiven him.
(יא) לֹ֖א תִּגְנֹ֑בוּ וְלֹא־תְכַחֲשׁ֥וּ וְלֹֽא־תְשַׁקְּר֖וּ אִ֥ישׁ בַּעֲמִיתֽוֹ׃
(11) You shall not steal; you shall not deal deceitfully or falsely with one another.
(יב) וְלֹֽא־תִשָּׁבְע֥וּ בִשְׁמִ֖י לַשָּׁ֑קֶר וְחִלַּלְתָּ֛ אֶת־שֵׁ֥ם אֱלֹקֶ֖יךָ אֲנִ֥י ה'׃

(12) You shall not swear falsely by My name, profaning the name of your God: I am ה'.

(יח) לֹֽא־תִקֹּ֤ם וְלֹֽא־תִטֹּר֙ אֶת־בְּנֵ֣י עַמֶּ֔ךָ וְאָֽהַבְתָּ֥ לְרֵעֲךָ֖ כָּמ֑וֹךָ אֲנִ֖י ה'׃

(18) You shall not take vengeance or bear a grudge against members of your people. Love your fellow [Israelite] as yourself: I am ה'.

Even though some of these parallels are a bit stronger than others, all of the mitzvot in this section can definitely be categorized according to one of the last five DIBROT.
We still have our question, i.e. we are missing a parallel for the third DIBBUR - LO TISA ET SHEM HASHEM ELOKEICHA LA-SHAV - in the ANI HASHEM ELOKEICHEM group.
Bothered by this question, Chizkuni (based on Vayikra Rabba 24:5) suggests that LO TISA is parallel to 'lo tishav'u bi-shmi la-shaker' (see 19:12).
However, that parallel would 'violate' the pattern that we discerned above, for the parallel should be found within the ANI HASHEM ELOKEICHEM group, i.e. in the first ten psukim.
Furthermore, based on the context of 19:12 - Lo tishav'u bi-shmi la-SHAKER - and noting the use of the word 'shaker' - its parallel to 'lo taaneh be-re'acha ed SHAKER' (Commandment #9) appears to be much more convincing. [This also keeps it in the ANI HASHEM group.]

(ה) וְכִ֧י תִזְבְּח֛וּ זֶ֥בַח שְׁלָמִ֖ים לַה' לִֽרְצֹנְכֶ֖ם תִּזְבָּחֻֽהוּ׃ (ו) בְּי֧וֹם זִבְחֲכֶ֛ם יֵאָכֵ֖ל וּמִֽמׇּחֳרָ֑ת וְהַנּוֹתָר֙ עַד־י֣וֹם הַשְּׁלִישִׁ֔י בָּאֵ֖שׁ יִשָּׂרֵֽף׃ (ז) וְאִ֛ם הֵאָכֹ֥ל יֵאָכֵ֖ל בַּיּ֣וֹם הַשְּׁלִישִׁ֑י פִּגּ֥וּל ה֖וּא לֹ֥א יֵרָצֶֽה׃ (ח) וְאֹֽכְלָיו֙ עֲוֺנ֣וֹ יִשָּׂ֔א כִּֽי־אֶת־קֹ֥דֶשׁ ה' חִלֵּ֑ל וְנִכְרְתָ֛ה הַנֶּ֥פֶשׁ הַהִ֖וא מֵעַמֶּֽיהָ׃

(5) When you sacrifice an offering of well-being to ה', sacrifice it so that it may be accepted on your behalf. (6) It shall be eaten on the day you sacrifice it, or on the day following; but what is left by the third day must be consumed in fire. (7) If it should be eaten on the third day, it is an offensive thing, it will not be acceptable. (8) And one who eats of it shall bear the guilt for having profaned what is sacred to ה'; that person shall be cut off from kin.

(ט) וּֽבְקֻצְרְכֶם֙ אֶת־קְצִ֣יר אַרְצְכֶ֔ם לֹ֧א תְכַלֶּ֛ה פְּאַ֥ת שָׂדְךָ֖ לִקְצֹ֑ר וְלֶ֥קֶט קְצִֽירְךָ֖ לֹ֥א תְלַקֵּֽט׃ (י) וְכַרְמְךָ֙ לֹ֣א תְעוֹלֵ֔ל וּפֶ֥רֶט כַּרְמְךָ֖ לֹ֣א תְלַקֵּ֑ט לֶֽעָנִ֤י וְלַגֵּר֙ תַּעֲזֹ֣ב אֹתָ֔ם אֲנִ֖י ה' אֱלֹקֵיכֶֽם׃

(9) When you reap the harvest of your land, you shall not reap all the way to the edges of your field, or gather the gleanings of your harvest. (10) You shall not pick your vineyard bare, or gather the fallen fruit of your vineyard; you shall leave them for the poor and the stranger: I ה' am your God.

The korban SHLAMIM is a voluntary offering that can be eaten by the person who brings the offering; however, its meat must be consumed on that same day or the next (see Vayikra 7:16-18). Parshat Kedoshim presents this law once again (see 19:5-8), adding the information that the punishment for eating the meat outside of this time frame is 'karet' - being 'cut-off' from the people of Israel (see 19:8!) - one of the most stringent of Biblical punishments.
Interestingly, the Rabbis interpret this prohibition in an even stricter fashion.
They claim that the primary prohibition is not necessarily eating the korban on the third day, but rather simply THINKING about eating the KORBAN outside of its time frame!
In other words, if at the time of offering this sacrifice, one merely thinks about eating its meat outside of its time frame - the offering is rendered PIGUL (disgusting, rejected) - and the one who does so will be punished with KARET! [Even if the meat is never eaten at the wrong time.]
This strange law raises three questions.
First of all, why would someone think of doing so in the first place?
Secondly, let's say they do, why is the punishment for simply 'thinking about it' so severe?
And finally, what is so terrible if one eats from this korban for an extra day?
Is it really better that they should let the meat 'go to waste'?
To understand the logic behind the law of PIGUL, we must consider that is quite impossible for a single person to consume the meat of an entire animal in a day or two. Therefore, practically speaking, the Torah's prohibition against eating the meat of this offering outside its time frame forces the individual to SHARE this meat with others!
Let's say that our assumption is correct that the owner of the offering has no choice other than to share it with other visitors. Consequently, we now have a logical reason for one to think of when they will eat this meat at the time of its offering. The very THOUGHT of eating an offering outside its time frame implies that the owner does not want to SHARE it with others.
In other words, this person offering the korban is being selfish, for they wants to save all of the meat for themself.
Clearly, being selfish is a bad trait.
But is it so evil that it deserves the punishment of KARET - to be totally cut off from the people of Israel?
This law of PIGUL may contain an extremely important teaching concerning the necessary balance between our relationship with God and people.
Recall that the Korban SHLAMIM is a voluntary offering where one wishes to express their closeness to God, to re-affirm their commitment to the covenant of HAR SINAI. If at the height of one's spiritual experience, as they stands in front of God making an offering, a selfish thought can still enter their mind - i.e. he does not want to share this korban with others - God becomes 'disgusted' with this person, and the korban becomes PIGUL/rejected.
A person who has yet to inculcate the basic trait of sharing, has no right to stand in front of the altar and offer a voluntary korban to God!
To support this understanding, note how the next verse in Parshat Kedoshim contains a law that stems from a similar reason. The obligation of the farmer to leave over a part of their field for the poor ['pe'a', 'shichecha', and 'leket' / see 19:9-10] teaches the owner not to be so selfish as to keep all of its produce for themself. Here we find yet another commandment that requires the sharing of prosperity, and thus supports our interpretation of the underlying reason for the law of pigul.
If 'sharing' is indeed the underlying reason for PIGUL and PE'A, then the parallel between Parshat Kedoshim and the Ten Commandments, as discussed above, would suggest that these laws should be in some manner related to the third Commandment of LO TISA - not to proclaim God's Name in vain.
To uncover that connection, we must return to our study of the meaning of God's Name in Genesis, and its connection to the laws of the MIZBEIACH and hence to korbanot in general.
Recall in Parshat Lech Lecha how Avraham Avinu, immediately upon his arrival in Eretz Canaan, built a MIZBEIACH and 'calls out in God's Name' in BET EL [lit. the HOUSE of God] (see Breishit 12:8 & 13:4).
Avraham's MIZBEIACH served as a vehicle enabling him to 'call out in God's Name', or as Ramban on 12:8 explained, teaching mankind concerning their need to recognize God and His Creation.
(ח) וַיַּעְתֵּ֨ק מִשָּׁ֜ם הָהָ֗רָה מִקֶּ֛דֶם לְבֵֽית־אֵ֖ל וַיֵּ֣ט אׇהֳלֹ֑ה בֵּֽית־אֵ֤ל מִיָּם֙ וְהָעַ֣י מִקֶּ֔דֶם וַיִּֽבֶן־שָׁ֤ם מִזְבֵּ֙חַ֙ לַֽה' וַיִּקְרָ֖א בְּשֵׁ֥ם ה'׃
(8) From there he moved on to the hill country east of Bethel and pitched his tent, with Bethel on the west and Ai on the east; and he built there an altar to ה' and invoked ה' by name.
(ד) אֶל־מְקוֹם֙ הַמִּזְבֵּ֔חַ אֲשֶׁר־עָ֥שָׂה שָׁ֖ם בָּרִאשֹׁנָ֑ה וַיִּקְרָ֥א שָׁ֛ם אַבְרָ֖ם בְּשֵׁ֥ם ה'׃
(4) the site of the altar that he had built there at first; and there Abram invoked ה' by name.
Later at Har Sinai we find a similar connection between the mizbeiach and 'shem Hashem' [God's Name]. Immediately upon the completion of the Ten Commandments, God commands Bnei Yisrael:
(כא) מִזְבַּ֣ח אֲדָמָה֮ תַּעֲשֶׂה־לִּי֒ וְזָבַחְתָּ֣ עָלָ֗יו אֶת־עֹלֹתֶ֙יךָ֙ וְאֶת־שְׁלָמֶ֔יךָ אֶת־צֹֽאנְךָ֖ וְאֶת־בְּקָרֶ֑ךָ בְּכׇל־הַמָּקוֹם֙ אֲשֶׁ֣ר אַזְכִּ֣יר אֶת־שְׁמִ֔י אָב֥וֹא אֵלֶ֖יךָ וּבֵרַכְתִּֽיךָ׃

(21) Make for Me an altar of earth and sacrifice on it your burnt offerings and your sacrifices of well-being, your sheep and your oxen; in every place where I cause My name to be mentioned I will come to you and bless you.

As the above examples show, the concept of 'shem Hashem' relates directly to the MIZBEIACH. In fact, the bet ha-mikdash itself is consistently referred to in Sefer Devarim as 'ha-Makom asher yivchar Hashem leshaken SHMO sham' - the place that God will choose to allow God's Name to dwell:
(ה) כִּ֠י אִֽם־אֶל־הַמָּק֞וֹם אֲשֶׁר־יִבְחַ֨ר ה' אֱלֹֽהֵיכֶם֙ מִכׇּל־שִׁבְטֵיכֶ֔ם לָשׂ֥וּם אֶת־שְׁמ֖וֹ שָׁ֑ם לְשִׁכְנ֥וֹ תִדְרְשׁ֖וּ וּבָ֥אתָ שָּֽׁמָּה׃
(5) but look only to the site that your God ה' will choose amidst all your tribes as God’s habitation, to establish the divine name there. There you are to go,
As the very purpose of the bet ha-mikdash and the mizbeiach is to properly publicize the Name of God, any law relating to the proper offering of a sacrifice could be considered as parallel to LO TISA, especially the laws of pigul.
If so, then our parallel between the DIBROT and opening psukim Parshat Kedoshim is complete, as pigul becomes the parallel for Lo Tisa in the 'Ani Hashem Elokeichem' section!
This parallel also follows the differentiation between the mitzvot bein adam la-Makom (first five) and the mitzvot bein adam le-chaveiro (last five). It should not surprise us now to find that the Torah's presentation of the of law of PIGUL includes the phrase -'et kodesh HASHEM chillel' - for they has desecrated that what is holy to God (see 19:8).
As the primary concept of the Third Commandment is not to desecrate God's Name, then its parallel could include any law that may cause God's Name (or reputation) to become tainted. An individual who comes to the bet ha-mikdash to express their special closeness to God - by offering a korban shlamim, yet at the same time thinks selfishly about themself, causes God's Name to be desecrated.
One could suggest that this may be the underlying message of the two sections of the Ten Commandments, [i.e the two LUCHOT of BRIT SINAI]. The mitzvot bein adam la-Makom' of the first five DIBROT come 'part and parcel' with the mitzvot bein adam le-chaveiro of the last five DIBROT.
In fact, the law of pigul forms a meaningful transition between these two sections, for it is a law relating to both humans & God, and their fellow humans. This necessary blend between one's worship of God and God's respect and care for one's fellow, so typical of the other laws of Parshat Kedoshim, should be the most prominent character of the Jewish nation.
When Am Yisrael act in this manner, they become a true AM KADOSH, a holy nation that truly testifies that God is KADOSH and God's Name is KADOSH. By doing so, they facilitate bringing 'shem Hashem' God's Name (and hence God's reputation) to humanity.