I find interesting when Moses asked for a name at coordinates Exodus 3: 14-15... the response seems to have been rendered three ways. I think people are thrown off track by desiring to derive an actual "name" as people understand names, since Moses asked for a name. Is it possible God expressed His nature and essence? Seems like a declaration.
As I understand, the four letters represent "I Am Who I Am" or some derivative thereof. Could the message in verse 14 simply be ''I Am'' the God of Abraham..." revealing to Moses that the God which seems to have been absent or silent during those years of slavery, is now present? The same four letters are used in those three places. Why do men translate in reaching for a name by inserting vowels aside from understanding what is expressed?
Let us consider: Who names themselves? We were named by our parents, we in turn name our children, animals and 'things' made by our hands. Did God actually name Himself? I think the response to Moses' inquiry was appropriate. We see God revealing bits and pieces of Himself and His will for mankind over the course of time.
Imagine a man asking in the presence of an earthly king "what's your name?" This would truly be quite inappropriate and a sign of insubordination or disrespect. I'm not suggesting Moses disrespected God, but simply asked so he would have an answer if the people were to ask (as it reads). Wouldn't that man address an earthly king according to his honored title(s) men historically have addressed earthly kings (your Majesty, your Highness, your Excellency, etc.)? God's mysterious and misunderstood response is quite appropriate, since He is Eternal and beyond description.
The establishment of authority and eternity seems appropriate in the response.