Do you think such a pharaoh would be allowed to get away with such a change? Certainly, the pharaoh was essentially a god in human form - but the Egyptians did not believe the gods were infallible and omnibenevolent; that being a Judeo-Christian formulation. The Egyptian gods fought, argued, and occasionally had attitude problems that they took out on people. The gods were not perfect, and neither was their representative.
Not to pick on him (well actually, yes), Akhenaten was a pharaoh and changed just about everything, made all kinds of proclamations, and even moved the administrative capital of Egypt to quite frankly the middle of nowhere. All these changes lasted pretty much until he died - at which point the "god's decrees" were all reversed or annulled in short order. Not only that, but there began a systematic destruction of any and all findable traces that Akhenaten ever existed at all. Why? Because he was weird and crazy. If you don't believe he was crazy, consider that most of the statues he commissioned of himself had breasts. Totally.
The Great Pyramid would've been a source of immense national pride for the Egyptians. Nothing any other contemporary culture did was as massive, tall, and imposing. I'd think they wouldn't allow some ego-driven blowhard to co-opt it as his own. If Ramesses II didn't do it, no one else would've - that's what I think.