Of course, it may never happen. If the Queen lasts as long as her mother, Charles will be 80 by the time he finally gets the throne. He may not last that long, we just don't know. Still, I reckon he will stick with the name, it's what he's been known as for as long as he's been alive. So, 'Charles III' gets my vote.
As for the new one, I'm rather hoping they choose something not seen before. Or perhaps, if its a girl, name her after her grandmother.
I'm sure I remember reading somewhere that he was planning to become George VII.