Who you think I am is completely irrelevant to who I am, that is something established by me from the inside if you will. It's done before the question whether

Who you think I am is completely irrelevant to who I am, that is something established by me from the inside if you will. It's done before the question whether an observer exists even arises. So yes, you wouldn't know either way, but that still doesn't make them Hamlet if they're not.