If God is God, then God is Creator, Impetus, Provocation, I could go on, but you get the idea. Nothing identifies God, because nothing stands outside God to make an objective perception. God just is.
If you wanna call that "state of being" "identity," go right ahead. Ain't no skin off my nose. It's just as good, if not better than a lot of other particular understandings we have of God. Some folks call it "the Creative Principle." Some call it "Reality." Some call it "Allah." Some call it "Myself."
Whatever you want to call it, it's there. It exists. it not only has being, it is Being -- Existence.
It's absolute. God "made the rules," because those, too, are absolute.
I think you're trying to reduce God to some kind of idea, or human construction, that must stand up to some kind of empirical test. What I'm saying is that God is Reason, God is Motive, God is Understanding. All those absolute things that we break down to their lowest common denominator and pin our existence and our sentience upon, we understand as God.
At the same time, because those things are God, they are greater that we can apprehend. We have life, but we don't know how to create life. We have minds, but we don't really understand how that self-cognizance originates. God is More than just the sum of those things.
For me, it's really more about a "system of understanding" than a belief. I couch that understanding in Christian theology, because that's what resonates with me.