What's in a Name?
(יג) וַיֹּ֨אמֶר מֹשֶׁ֜ה אֶל־הָֽאֱלֹהִ֗ים הִנֵּ֨ה אָנֹכִ֣י בָא֮ אֶל־בְּנֵ֣י יִשְׂרָאֵל֒ וְאָמַרְתִּ֣י לָהֶ֔ם אֱלֹהֵ֥י אֲבוֹתֵיכֶ֖ם שְׁלָחַ֣נִי אֲלֵיכֶ֑ם וְאָֽמְרוּ־לִ֣י מַה־שְּׁמ֔וֹ מָ֥ה אֹמַ֖ר אֲלֵהֶֽם׃

And Moses said to God, "Behold I come to the children of Israel, and I say to them, 'The God of your fathers has sent me to you,' and they say to me, 'What is His name?' what shall I say to them?"

(א) מה אומר אליהם - כי איני מכיר ויודע שמך המיוחד.
(1) מה אמר אליהם?, seeing that I do not know Your specific name.
(א) ואמרו לי מה שמו הנה השם יורה על הצורה האישיית, והצורה היא סיבה עצמיית לפעולה המיוחדת לאיש. יאמרו אם כן באיזה פועל נמשך ממנו, שבו יקרא בשם מי ששלחך לה וציא נו:
(1) ואמרו לי "מה שמו?", a name describes the individual features of a person, Being, or what makes him distinctive. The people could therefore be expected to ask Moses in what manner this G’d whose messenger he claimed to be had distinguished Himself as being special, different from other gods.

Ramban - Nachmanides (1194–1270) Sephardic rabbi, philosopher, physician, kabbalist, and commentator. "They will say to me: What is His name? What will I say to them?": This name [Eh-yeh Asher Eh-yeh] contains the answer to Moses' question to G-d, as we have explained. Moses asked by what divine attribute is his mission to them, whether with the attribute of [the name] E-l Sha-dai, which stood by the Patriarchs, or with the supernal attribute of Mercy, with which signs and wonders will be performed to speed their redemption. He informed Moses that he [Moses] is being sent to them with the attribute of Justice which is within the attribute of Mercy, suggesting that the miracles which will be done on behalf of their deliverance from the bondage will at the same time be acts of judgment against the Egyptians. This is the sense of "Eh-yeh Asher Eh-yeh": "I will be (in judgment) that which I will be (in mercy)."

"And then G-d said to Moses, 'Thus should you say to the children of Israel: Eh-yeh sent me unto you'": thus teaching the unity [of the two attributes, which explains why the divine name is not mentioned here twice]. "Thus should you say to the children of Israel: 'The Eternal [the name Havayah] sent me to you'," for this Name [Havayah] indicates the attribute of Mercy, and thus they will know "that He hath caused His glorious arm to go at the right hand of Moses" (Isaiah 63:12) and He will make new signs and wonders in the world. Thus G-d explained to Moses that the name Eh-yeh אהיה ,which He commanded him to tell the children of Israel, corresponds to this Great Name יהוה [the name Havayah] and that they are alike in language [as both signify eternal existence] and in letters, for the two final letters of the first name [Eh-yeh] constitute the first ones in Havayah. And may the Holy One, blessed be He, show us wonders in His Torah.

(יד) וַיֹּ֤אמֶר אֱלֹהִים֙ אֶל־מֹשֶׁ֔ה אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה וַיֹּ֗אמֶר כֹּ֤ה תֹאמַר֙ לִבְנֵ֣י יִשְׂרָאֵ֔ל אֶֽהְיֶ֖ה שְׁלָחַ֥נִי אֲלֵיכֶֽם׃

God said to Moses, "Ehyeh Asher ehyeh (I will be what I will be)," and He said, "So shall you say to the children of Israel, 'Ehyeh (I will be) has sent me to you.'"

(א) אהיה אשר אהיה. אהיה עמם בצרה זו אשר אהיה עמם בשעבוד שאר מלכיות אמר לפניו רבונו של עולם, מה אני מזכיר להם צרה אחרת דים בצרה זו. אמר לו יפה אמרת, כה תאמר וגו' :

(1) I Am as I Am - I will be with them in this time of distress just as I will be with them during the suppression of other kingdoms. [Moshe] said, "Master of the Universe, why do I need to mention other distress? This travail is sufficient!" He said to him, "You have spoken well. This shall you say, etc."

(א) ויאמר אלהים אל משה - אם אינך יודע שמי אני אומר לך, כי שמי אהיה לעולם ויכול אני לקיים מה שאני מבטיחך. ומעתה שאמרתי לך כי שמי אהיה. כה תאמר לישראל אהיה שלחני אליכם.

"God said to Moses...": if you do not know My Name, I will tell you that I am the Eternal. This means that I can fulfill any promise I make. Now that I have told you that My name is “the Eternal,” כה תאמר, thus you shall say to the Children of Israel, “the One Who is the Eternal has sent me to you.”

(א) אהיה אשר אהיה ההוה תמיד על ענין אחד מצד עצמו, ומזה יתחייב שיאהב המציאות וישנא כל הפסד מנגד למציאות, כאמרו כי לא אחפוץ במות המת ומזה יתחייב שיאהב משפט וצדקה, אשר תכליתם מציאות, וישנא העול והאכזריות, המטים עקלקלות אל העדר והפסד, ובזה שנא חמס ואכזריות המצרים נגדכם:

"I Will Be What I Will Be...":

I am an independent existence, not subject to influences by other phenomena or even caused by them. And from this I obligate myself to I love all that is in existence, and to despise all that goes against existence. I deeply resent anything or anyone who tries to terminate such an existing being from continuing to do so. The prophet Ezekiel said, “for I do not desire the death of him that dies.” From this it follows that I must love righteousness and justice. he objective of both virtues being the continued existence of all who deserve it. At the same time, it follows that I must hate injustice and cruelty as these vices are apt to terminate the existence of the victims of these vices. Clearly, then, this G’d must hate the violence and cruelty perpetrated on you by the Egyptians.

וַיְדַבֵּר אֱלֹהִים אֶל מֹשֶׁה וַיֹּאמֶר אֵלָיו אֲנִי ה'. וָאֵרָא אֶל אַבְרָהָם אֶל יִצְחָק וְאֶל יַעֲקֹב בְּאֵל שַׁדָּי וּשְׁמִי ה' לֹא נוֹדַעְתִּי לָהֶם.

And God spoke unto Moses, and said unto him: ‘I am the LORD; and I appeared unto Abraham, unto Isaac, and unto Jacob, as El Shadai (God Almighty), but by My name the Lord was not known to them.

"The Almighty had made a promise to the Patriarchs. He had promised them the land of Canaan but the time had not been ripe for its fulfillment. This is the meaning of the phrase that God had not yet appeared to them by His name. The attribute of Divine fulfillment implied in this name of God had not yet been realized in history (Nechama Liebowitz)

Talmud Sanhedrin 111a "I appeared unto Abraham": Said the Holy One blessed be He to Moses: Alas for those who are gone, never to be replaced (in reference to the Patriarchs)! Many times I revealed myself to Abraham, Isaac and Jacob as God Almighty (El Shadai), but I did not make known to them that My name as I have told you and they did not question my ways. I said to Abraham: (Gen 13) "Arise and go forth in the land the length and breadth...for to thee shall I give it" - He sought to bury Sarah and did not find where, until he purchased a place with money - yet he did not question my ways." I said to Isaac (Gen 26): "Dwell in this land...for to thee and thy seed shall I give all these lands" - He sought to drink water and did not find, "And the shepherds of Gerar strove with the shepherds of Isaac" - yet he did not question my ways. I said unto Jacob (Gen 29): "The land which thouh liest on, to thee will I give it and unto thy seed" - He sought a place to pitch his tent and did not find until he acquired it for a hundred kesitah - yet he did not question my ways, and did not ask Me what was My name as you have asked....

Rambam Maimonides God appeared to the Patriarchs as the Prime Mover behind all natural events. His miracles were apparent to them without recourse to violating the natural order. In times of famine He redeemed them from death and in war from the sword and provided them with wealth and honor and every good thing. These things, like all the promises in the Torah of blessing and curse, are not meted out to a man as his due, as a reward for good deeds and punishment for sin. They constitute miracles (of Divine grace). Man's own deeds do not automatically give rise to favorable effects or otherwise. But the reward and punishment alluded to in the Torah in this world are in the nature of miracles, hidden ones which the onlookers regard as the workings of nature. But in reality they are the providential allocation of reward and punishment. God said to Moses: I appeared to the Patriarchs as One who assists His chosen ones through the might of my hand (but without violating nature). By My ineffable name expressing the essence of all existence (Exodus 3:14) I was not known to them to introduce innovations changing the natural course of events. Therefore tell the Children of Israel that I am the Lord and let them know My great name through which I shall perform for them wonders that they may know that I am the Lord who does these things.

Rabbi Arthur WaskowAs Moses faces the unquenchably fiery Voice Who is sending him on a mission to end slavery under Pharaoh, he warns the Voice that the people will challenge him: “Sez who?” And the Holy One, the Wholly One, answers: “Ehyeh Asher Ehyeh, I Will Be Who I Will Be” –- a fitting Name for a universe that is always Becoming. A universe in which the powerless poor can be empowered and the pharaoh’s power can dissolve like powder into the Sea of Reeds. Then God adds, “But that’s a mouthful. You can use just ‘Ehyeh, I Will Be,’ as my nickname, if you like.”
“And oh yes, you can also call me ‘YHWH.’" But we actually can’t. There’s no way to “pronounce” those letters, with no vowels. And for a couple of millennia, Jews have been strictly taught not even to try pronouncing it but instead to say “Adonai, Lord.”