One of the first decisions kings make when they ascend the throne is what their name will be. His grandfather, for instance, was Albert but chose the name George as his regnal name. (Very popular with that family although I can’t think why. Most of the Georges were perfectly dreadful rulers, as incompetent as they were short-sighted).
There was talk some years back that Charles’ admiration for George III (right, go figure) was leaning him towards George. Any more recent clues as to what his decision might be? I guess he could go with Charles III but there’s been a pretender king of that name so I think it unlikely. (Bonnie Prince Charlie styled himself Charles III when his father James, the Old Pretender, - son of James II - died.)