He MAy want to.... If he does, really want to, I'd say he's perfectly entitled..
I assume he could even legally change his name right now just like any other citizen if he really wants to - but that is evenmore unlikely (choosing a different regnal name is a possibility, it's all up to him)
I personally really hope he chooses to go by Charles, no reason to do away with the name all together for Monarchs. But given his popularity and what happened to Charles I I would understand if he chooses to go with George.
TBH when Charles ascends the throne I don't think his regnal name will be as interesting to the public as what Camilla's title will be.