What if there is a Supreme Being…
But that this Supreme Being is not the God of Abraham?
Not Yahweh?
Not "God", but "The Supreme Being"?
What if there is a God but Yahweh doesn’t exist?
The name YHVH is a reference to "being; existence itself" while the name/title Elohim references power itself. In other words, without Elohim, nothing in the Universe would be able to
do anything because there would be no energy, momentum, work, force, etc. If you like you can think of Elohim as immense power of the singularity that preceded the Big Bang, that which led to the strong, week, electromagnetic, and gravitational interactions we see in physics today, as well as the Power that set off that singularity's expansion in the first place. Because of Power (Elohim), the myriad things have the power to do, which is to say, interact. Many peoples in the Levant and Mesopotamia venerated a power they envisioned as a deep underground aquifer that lent it's virility to the land thus making it what we would call fertile (though fertility is associated with the female genitive power, and these people saw it the other way around: land is barren, but water makes it virile). This abyss, or for others just rivers and springs themselves, were often seen as with divine seminal fluid. In Genesis 1:2 the Hebrews asserted that even the virile power of the Deep came from that aspect of "God" which is Power itself. The word רָחַף [rachaph], which is often translated to "hover" or "move" means "to flutter, to shake, to brood." "The breath of Elohim was shuttering/brooding over the face of the waters" (the waters being those of the Deep referenced earlier in the same line) can be read to mean that Power itself ejaculated power into the Abyss. Which implies that even this aquifer that some venerate is a lesser power than YHVH Elohim, a stance that neighbouring cultures would not have been happy to hear. The Hebrews were claiming that if people are going to worship "the most powerful thing" they should worship YHVH Elohim.
Anyway, back to the name YHVH. Just as Elohim is the Power from which all power derives, YHVH is Existence from which all existing things derive their lack of non-existence. If Elohim is the power that preceded the Big Bang, YHVH is existence which preceded it. It's hard for us to conceive of anything as existing before there was spacetime or matter/energy, yet existing things cannot be the effect of nonexistent causes. So, there must have always have been at least one thing in existence for anything else to have an existence. This is YHVH.
So, when you ask, "What if there is a God, but not YHVH?" you are really asking, "What if there is a God, but not Existence itself?" There could not be any God or anything else if there is no Existence. You suppose that this God would be the Supreme Being, which is Elohim by definition. But what use is Power, if it doesn't exist?
As an aside, the fact that the Hebrews called this Power Elohim and Existence YHVH is purely based on their linguistics. The names would differ in different cultures. For example, in India these are called Prakriti & Purusha, respectively, and are personified as Shakti & Shiva.
