His full name is Charles Philip Arthur George.
So he could be Charles III, Philip II, Arthur (the prior "King Arthur" is considered legendary, prior to the birth of the modern nation in 886 under Alfred the Great), or George VII.
And Charles might be interesting, since the previous kings of that name were both of the House of Stuart. That might be problematic, as his ancestor George I is the one that took the throne from the Stuart's, after the death of Anne with no direct heirs. Then the name was Hanover, changed to Saxe-Coburg and Gotha under Edward VII (his father's family name), then finally under Edward VIII to Windsor after the King severed all ties with the Saxe-Coburg name and titles during WWI.
If I was to guess, he would probably choose George. Philip is also a possibility to honor his father.