"And they shall say unto me: What is His name? What shall I say unto them?" (Ex. 3:13)
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 (new phenomena in Creation) 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."
He will make new signs and wonders in the world….
"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].
It is for this reason that G‑d commanded Moses yet further: "Thus should you say to the children of Israel: 'The Eternal [the name Havayah]...hath sent me unto 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,which He commanded him to tell the children of Israel, corresponds to this Great Name [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.
[Adapted from Rabbi Dr. Charles Chavel's annotated translation.]