Yahweh. He will be that He will be.
Generally, the debate is over whether the divine name should be understood ontologically or covenantally. I see no problem with both but I think the name is meant to be heard in a covenantal context, first and foremost.
Ontologically, the name speaks to God's self-sufficiency. He does not owe His existence to anything else. Whereas all of creation only continues to exist on the contingency of God holding it together. Even we owe our continued existence to other created things, such as food, water, etc, but all of these ultimately come from God, the only uncreated and eternally self-existing one. This is why questioning the existence of God is so foolish. He is ontologically more real than even we are.
Covenantally, God's chosen people are to know Him by His divine name. It is interesting that the name was glossed over in tradition as 'Lord' when God states explicitly that His people are to know Him by His name. Within trinitarian orthodoxy, YHWH is applied to the Divine Nature, which means it can be equally applied to any of the three divine persons who share the same Divine Nature. So when the Apostles identify Jesus as Yahweh, or when Jesus identifies Himself as Yahweh, they are claiming that He truly is God.
