The answer is a cryptic elaboration on the previous reply "I (am/will
be) with you". In thinking about this answer 'I am who I am',
I reflected on the situation when I do something untypical of myself.
I say "that's not like me! I'm not like that!".
The first thing then about this reply is perhaps it says that God
always acts like himself, he always is what he is, he is consistent
in his character. (The Greek translation "I am he who is" ie "who
eternally is because of what he is", would introduce inappropriate
philosophical ideas.) In Exodus 6:3 God relates how he revealed
himself as competent and able (El shaddai) to do what he promised for
the Patriarchs. This text in Exodus 3 may now reveal that his name
Yhvh has a specially *redemptive* context, he does not change, he is
*always with his people to redeem them*.
Secondly, the name of God is explained in verbal form, eg "say 'I am'
has sent you". This uses a verb as a noun and perhaps hints that the
personal name of God - Yhvh, could also be derived as verbal in form
rather than as a normal noun.
The verb havah occurs in the Hebrew OT meaning "to become". Conjuring
a pre-formative on the verb havah to make a noun yahveh as Albright
did opens a door for the following speculation. Correct me if I err
here but the normal (qal) imperfect of havah should be yihveh and the
causative (hiphil) imperfect should be yahveh.
As a verb yahveh would mean "he causes to become" ie "he creates".
Thus the name *Yahveh* would mean *creator* (In Genesis 1:1 we find
bara' Elohim ie "God created" but in Genesis 2:4 ff we find Yhvh
forms, plants etc so the idea of creation is already present in
Yhvh).
The surprise word play arises because the Exodus 3 text doesn't
emphasise the expected creation aspect of Yhvh and say
*ahveh asher ahveh* using the causative of havah,
(I cause to be what exists), it says
*ehyeh asher ehyeh*
(I am who I am) using the normal imperfect of hayah (to be).
The point then may be to add to the context of Yhvh as meaning
*creator* his character as *always being there to redeem*.
cheers
Peter