Tbh, I think that's perfectly fine. We all know that cat's are gods anyway ;D
As you said, it's more of a title than an actual being.
Like, the Christianity's all mighty god is "THE" god, there's no gods beside that one (but that's kind of weird imo). In Old Norse mythology, who WASN'T A GOD? (like, seriously...)
But what I'm trying to say is: if the cat behaves like a god, why not name it "God"?
(I thought it was a funny name to have on a cat, I love it when people name their pets titles, like roomie, husband, wife or something else like that, it can mess with others so BADLY, I love it. Go ahead and name the imaginary cat God, please<3)