What name of G-d was Moshe supposed to relay to B'nai Yisra'el?

Question

View Shmot 3:13-15.

In verse 13, Moshe asks G-d what name of G-d should he tell B'nai Yisra'el.

In verse 14, G-d first answers I AM THAT I AM, and then says just I AM.

Fine, I am aware of Rashi's explanation of the conversation Moshe had with G-d regarding omitting "that I AM".

But, in verse 15, G-d says, "G-d, G-d of your fathers, Avraham, Yitzhak and Ya'akov..." and finally the verse ends, "THIS is my name..."

What is the meaning of G-d apparently giving Moshe different answers to what seems like a simple question? Is Moshe supposed to relay all these names? If it's just one, which one is it?

Answer 1

The Ohr HaChaim (end of commentary to verse 15) writes that Moshe was supposed to first tell them "I AM sent me" and then tell them "G-d, G-d of your fathers, Avraham, Yitzhak and Ya'akov sent me."

He gives several explanations for what was being communicated with the name "I AM," but whatever the idea of "I AM" is meant to be, it was an unknown name to the Jewish people. Therefore, Moshe was to follow up with the name that they all know and are familiar with, to authenticate Moshe's claim that Hashem had sent him.

Answer 2

It seems that the Chizkuni may have had your question. On 3:14 he says,

The first “ I AM” is the name and the second is the explanation. So it means,

'My name is “ I AM” because I am and will endure for ever and ever without end and I am with them in that I will redeem them from the burdens of Egypt.'

FYI please see the rest of the Chizkuni's commentary.