To understand it as a positive name, in the manner you are suggesting here, is on an Islamic reading, inaccurate. Reading the story, God’s answer to Moses (pbuh) seems to be, I am what I am…who are you to ask me for a name…You think I can be named? It is a way of telling the reader that they misunderstand the purpose of the “name” if they think it somehow names God.
What Judaism does with this is brilliant. How do you speak of what is beyond our knowledge and thus beyond every name. You (anti-)name it and never speak it. You make a mark that deflects speech and knowledge at the very instant where you crave it above all else.
I am not claiming exhaustive knowledge of Judaism here. But I do know for instance that Maimonides treats the import of the tetragrammaton as entirely negative: it is a way of resisting naming God, because God cannot be named. The tetragrammaton is largely absent in a major twentieth century Jewish thinker like Rosenzweig (I can’t remember an instance of it in The Star, that doesn’t mean it isn’t there, but if it is, the idea doesn’t play much of a role one way or the other) … and Levinas again, not surprisingly, uses it as a negative non-naming: a way of gesturing at the transcendence and unknowability of the divine essence.
(You can see a different tradition in Buber who uses the Tetragrammaton to emphasize that God is always near; but in order to do this Buber has to attack the Jewish tradition of not pronouncing the “name”. I am sure there probably are precedents for Buber’s interpretation. But I have no idea what they are. I take his read to be a departure from the mainstream of the Jewish intellectual tradition on this point…Rosenzweig snarkily refers to Buber’s early work as “Atheistic Theology”).
In Judaism and in Christianity, the Name of God is so revered and so considered sacred, so above every other name, that it is never used like a human name. We use our names casually, but God’s Name is above our names, so we do not speak His Name.
Moreover, the Name of God is impossible to be comprehended, even in ancient Hebrew. In the Hebrew Scriptures, the Divine Name is an acronym (YHWH), because the Hebrew tongue dose not include vowels. Hence, you can’t actually say what the Name of God is; it is a mystery. Some people have attempted to spell out God’s Name, to discover who God is, but God is in Himself a mystery, He is incomprerendable, so no one can truly comprehend His Name, the Name which is God’s Identity, God Himself. The best man can discover is that the Divine Name means “I am who I am” and “I will be what I will be”, i.e., ‘God is God’ and ‘God is with us’. The Name which God has given is both a name and no name: on one hand, God has revealed who He is, but, on the other hand, He has also revealed the abyss betwen God and man - which gives further understanding of who God is. He is both near and far, the God who alone is God and who is always with us, in us and we in Him, but who is so holy that an infinite abyss is between Him and us, and yet this abyss is filled with His Mercy.
In the Bible, the Name of God is replaced with the name “The Lord”. For example, “I am the Lord, your God” and “Lord, I believe; help my unbelief!” This is the name which Jews and Christians use in place of God’s Name, out of reverence, in light of the Second Commandment. The name “The Lord” basically means ‘King’ or ‘Sovereign’; it shows the absolute lordship and sovereighty of God over all things, even false gods (in ancient times, a god was believed to be one among equals in the world, since all gods were believed to be real, but that wasn’t the case with God; God is the God of gods, He is above all gods, because no god exists save He).