Let us assume that an omnipotent god exists. He by definition can do anything that is logically possible. So if it is logically possible to prove that a being is omnipotent then an omnipotent god can prove to himself that he is omnipotent.
So we just need to show that it is logically possible to prove that a being is omnipotent, to show that an omnipotent god can find out that he is omnipotent.
Can anyone show that it is indeed possible to prove that a being is omnipotent?
I don't think it is possible. Like he can ask a question "Can I stop time?" and he will find out that he can. Next, he can ask "Can I create 1 more time dimension?" and he will find out that he can. Next, he can again ask "Can I create 1 more time dimension?". He can keep on asking that question. He also can ask "Can I find out whether this hypothesis is correct or false or undecidable in our axioms?" (This hypothesis can be any mathematical hypothesis. There are infinite of them). If he can not do something that is logically possible then he will have found that he is not omnipotent. So it is easy to prove nonomnipotence. So it seems to me that an omnipotent being can never understand that it is omnipotent.
Edit:Please do not answer this question with your own definition of Omnipotence. Here I clearly mentioned that omnipotence is bound by logic. That is the definition I am using.