Just to add.. as for some people having different names in different cultures: Ramses is a good example.
He is Oxymandias in Greek
His "Horus" name was Ka-nakht-mery-Ra (the Strong Bull)
His Nebty name was Mek-Kemet-waf-khasut (Protector of Kemet)
His throne name was User-Maat-Ra-setep-en Ra
And his actual full birth name is Riyama-shisha-miamana
That last full name is why David Rohl, for example says the Pharoah "Shishak" is actually Ramses II, and not the Pharoah Shoshenq as mainstream scholars insist. He insists the Israelites were just shortening the "Shisha" in his longer name to "Shishak".
Ramses is another shortened form of the birth name obviously.
But to get back to the point, Moses, if he was in the royal court, probably wasn't simply called Moses.