Monarchs chose different names back when royalty was known by their titles - not their names. Nobody referred to a Prince Edward or a Prince George.
Edward VIII was always just the Prince of Wales and his brother was referred to always as just the Duke of York. There was only one Prince of Wales or Duke of York so there was no chance that just using the title would cause an identity crisis.
I'm reading right now a marvelous short story by Isak Dinesen about a singer who shared the same tutor as the Crown Prince of Denmark and for the life of me, I can't figure out which Crown Prince she's talking about. Back then, the titles were all that mattered.
In an age where the royals were just known by their titles, it was easy enough for a newly ascendant King to substitute one name for another. A George for an Albert, etc. But now its different - Charles is Prince of Wales but nobody refers to him as just the Prince of Wales - he's Prince Charles. He's called Charles on the news, in the forums, everywhere. It would be a big jump to go suddenly from being known as Prince Charles to King George.