We're not sure if this will be King George VII or King George VIII either.
Charles has said that when he's coronated, he'll probably change his name to George.
Actually, Charles had issued a
non-denial denial leaving open the possibility. Still if he does decide to not be Charles III, George VII is the only logical choice. I can't see him or any English monarch being brash enough to reign as King Arthur and being crowned King Philip II would bring up a thorny bit of history.
Prince William is pretty much stuck with being William V, as Philip, Arthur, and Louis are not really viable options.
Only time will tell if Prince George chooses to reign as King Alexander IV or not.