Then Moses said to God, "If I come to the people of Israel and say to them, 'The God of your fathers has sent me to you,' and they ask me, 'What is his name?' what shall I say to them?"
God said to Moses, "I AM WHO I AM." And he said, "Say this to the people of Israel, 'I AM has sent me to you.'"
Moses’ encounter with God in the burning bush was a unique call for a unique purpose: Moses was the man God created to deliver Israel from Egypt and bring them back to the land promised Abraham so long ago. Moses’ desire to know God’s name could mean that Israel had forgotten this truth. God’s revelation of His name to Moses would be a founding wall of Judaism that lasts to this day. The significance of The Name can be discerned from this ESV Study Bible note on Exodus 3:13-14:
I am who I am. In response to Moses' question (“What is [your] name?” v. 13), God reveals his name to be “Yahweh” (corresponding to the four Hebrew consonants YHWH). The three occurrences of “I am” in v. 14 all represent forms of the Hebrew verb that means “to be” (Hb. hayah), and in each case are related to the divine name Yahweh (i.e., “the Lord”; see note on v. 15). The divine name Yahweh has suggested to scholars a range of likely nuances of meaning: (1) that God is self-existent and therefore not dependent on anything else for his own existence; (2) that God is the creator and sustainer of all that exists; (3) that God is immutable in his being and character and thus is not in the process of becoming something different from what he is (e.g., “the same yesterday and today and forever,” Heb. 13:8); and (4) that God is eternal in his existence. While each of these points is true of God, the main focus in this passage is on the Lord's promise to be with Moses and his people. The word translated “I am” (Hb. ’ehyeh) can also be understood and translated as “I will be” (cf. esv footnote). Given the context of Ex. 3:12 (“I will be with you”), the name of Yahweh (“the Lord”) is also a clear reminder of God's promises to his people and of his help for them to fulfill their calling. In each of these cases, the personal name of God as revealed to Moses expresses something essential about the attributes and character of God.
To know God at this level is to know God at the core of His attributes and character. It is the very person of God for Him to be the self-existent, always existing One. And this God who called Moses into leadership and loved Israel is the same God Who calls me into service and loves the world in Jesus.