It doesn't have to be a former king's name, but it would be very unusual for him to choose something other than one of his own middle names, if he doesn't want to use his first name. The current Queen's father's first name was Albert (Bertie to the family) but he chose to use George, one of his middle names, when he came to the throne (my understanding is that Queen Victoria, whose husband was Prince Albert, asked that there never be a King Albert as her husband was not king).
I expect at this point Charles will use his first name if he comes to the throne, just because he is known so commonly by that name already. In times past, without the media interest and global communications that we have now, the general public didn't know very much about members of the royal family. But Prince Charles is known the world over as Charles -- it would be very strange for him to be called something else at this point in his life. Also, if he had come to throne at a younger age he might have considered it, but I would be surprised if he changes his name at this point.
Charles's names are Charles Philip Arthur George -- he's not going to use Philip, as that's his father (and see above about not having a King Philip when the current queen's husband was a prince), and he's not going to use Arthur (King Arthur? I don't think so), so his choices really are Charles or George. I expect he'll stick with Charles.
