Reputation: Critically Important and Utterly Trivial

רַבִּי שִׁמְעוֹן אוֹמֵר, שְׁלשָׁה כְתָרִים הֵם, כֶּתֶר תּוֹרָה וְכֶתֶר כְּהֻנָּה וְכֶתֶר מַלְכוּת, וְכֶתֶר שֵׁם טוֹב עוֹלֶה עַל גַּבֵּיהֶן:

Pirkei Avot 4:13

Rabbi Shimon said: There are three crowns: the crown of torah, the crown of priesthood, and the crown of royalty, but the crown of a good name supersedes them all.

קהלת ז׳:א׳

(א) ט֥וֹב שֵׁ֖ם מִשֶּׁ֣מֶן ט֑וֹב וְי֣וֹם הַמָּ֔וֶת מִיּ֖וֹם הִוָּלְדֽוֹ׃

Ecclesiastes 7:1

(1) A good name is better than fragrant oil, and the day of death than the day of birth.

רש"י על קהלת ז׳:א׳:א׳

טוֹב שֵׁם מִשֶּׁמֶן טוֹב. יָפֶה לְאָדָם שֵׁם טוֹב מִשֶּׁמֶן טוֹב. וּבְיוֹם הַמָּוֶת טוֹב הַשֵּׁם מִיּוֹם הִוָּלְדוֹ לְכַךְ הֻקַּשׁ שֵׁם טוֹב לְשֶׁמֶן יוֹתֵר מִשְּׁאָר מַשְׁקִין, שֶׁהַשֶּׁמֶן אַתָּה נוֹתֵן לְתוֹכוֹ מַיִם, וְהוּא צָף וְעוֹלֶה וְנִכָּר, אֲבָל שְׁאָר מַשְׁקִים, אַתָּה נוֹתֵן לְתוֹכָן מַיִם, וְהֵם בּוֹלְעִים.

Rashi on Ecclesiastes 7:1:1

Better a good name than precious oil. A fine reputation for a person is better than precious oil, and on the day of [his] death that reputation is better than [it was] on the day he was born. For this reason, a good name is compared to oil in preference to other liquids, for [if] you put water into oil, it rises and floats, and is distinguishable, but other liquids, [if] you put water into them, it becomes absorbed.

משנה אבות ב׳:ד׳

. הִלֵּל אוֹמֵר, אַל תִּפְרֹשׁ מִן הַצִּבּוּר, וְאַל תַּאֲמִין בְּעַצְמְךָ עַד יוֹם מוֹתְךָ,

Pirkei Avot 2:4

(4) Hillel said: do not separate yourself from the community, Do not trust in yourself until the day of your death,

Alternatively, a fine reputation is better on the day of death than on the day of birth, because so long as one lives, his reputation is subject to possible future deterioration, whereas on the day of death there are no uncertainties. This thought is found in the Mishnah in Avos 2:4 wherein Hillel said, “do not believe in yourself until the day you die.” (Sforno) Or, it is good for one to consider his death [יום המות], beginning from the time that he is born [יום הולדו], and by doing so he will refrain from sinning. (Khilos Yaakov)

Alex Lickerman M.D.
Your reputation lives a very real existence apart from you, representing the collective mental construct everyone but you shares about you, a construct based partially on your own actions but also on the perceptions others have about others' perceptions of your actions.
...Our reputation represents the way others look at us and as such, is at once critically important and utterly trivial.

משלי כ״ט:כ״ה

(כה) חֶרְדַּ֣ת אָ֭דָם יִתֵּ֣ן מוֹקֵ֑שׁ וּבוֹטֵ֖חַ בַּיהוָ֣ה יְשֻׂגָּֽב׃

Proverbs 29:25

(25) The fear of man become a trap for him, But he who trusts in the LORD shall be safeguarded.

סידור נוסח עדות המזרח, סדר השכמת הבוקר, מודה אני ד׳

(ד) מוֹדֶה אֲנִי האשה אומרת: מוֹדָה לְפָנֶיךָ מֶלֶךְ חַי וְקַיָּם שֶהֶחֱזַרְתָּ בִּי נִשְׁמָתִי בְחֶמְלָה, רַבָּה אֱמוּנָתֶךָ:

Siddur Edot HaMizrach, Preparatory Prayers, Modeh Ani 4

(4) I am thankful before You, living and enduring King, for you have mercifully restored my soul within me. Great is Your faithfulness.

בראשית א׳:כ״ז

(כז) וַיִּבְרָ֨א אֱלֹהִ֤ים ׀ אֶת־הָֽאָדָם֙ בְּצַלְמ֔וֹ בְּצֶ֥לֶם אֱלֹהִ֖ים בָּרָ֣א אֹת֑וֹ זָכָ֥ר וּנְקֵבָ֖ה בָּרָ֥א אֹתָֽם׃

Genesis 1:27

(27) And God created man in His image, in the image of God He created him; male and female He created them.

Alex Lickerman M.D.
Caring about our reputation doesn't mean we need others to like us. It means recognizing that as human beings we often can't help judging a book by its cover and that as long as the book itself is good, there's nothing wrong with caring about having an attractive cover around it.