I am who I am

I am who I am is a common modern translation of the Hebrew expression  אֶֽהְיֶה אֲשֶׁר אֶֽהְיֶה  hayah 'asher hayah taken from Exodus 3:14, referring to the God of the Hebrews.

Identifying God
Moses asked: “Suppose I am now come to the sons of Israel and I do say to them, ‘The God of your forefathers has sent me to you,’ and they do say to me, ‘What is his name?’ What shall I say to them?”—Exodus 3:13.

Moses question raises the point that God has a name. God’s Divine name had been considered so holy, that the Rabbinic practice of its removal affected how modern Bible translations used the Tetragrammaton. They typically replace God's personal name with titles, such as “LORD” and “God”.

Meaning of God's name
Since the Hebrews, under Egyptian servitude, already knew the name of God: YHVH (Jehovah), what God told Moses was the meaning of his Divine name. Where the "I am" translates from הָיָה hâyâh (Strong's H1961), according to Strong's definition, hayah is "always emphatic, and is not a mere copula or auxiliary." Therefore, the meaning of God's name, "Jehovah", can be understood to mean “He Causes to Become”.

To gain a real sense of the "emphatic" hayah expression, some Bible lectures have been quoted saying: These expressions were conveyed to show that God chooses to become, whatever is needed to fulfill His promises. So for the Israelites, no matter what obstacle loomed before them, or how difficult the predicament, Jehovah would become whatever was needed to deliver them from slavery and bring them into the Promised Land. This was confidence in God Moses was asking about to move the hearts of a people who already knew His name to be Jehovah.
 * "I will be what I will be"— See footnote in NIV''
 * “I shall prove to be what I shall prove to be.”
 * “I Will Become whatsoever I please.”
 * “Whatever the situation or need . . ., God will ‘become’ the solution to that need.”

Source

 * cl, “Look! This Is Our God”, p.9-10