Being royal apparently requires a fancy title and an even fancier surname, judging by the Mountbatten-Windsors.
In fact, William’s kids are Cambridges in school, rather than princes and princesses (viaExpress).
Still no surname in sight, though.
During his time in school and with the army, the Duke went by William Wales.
He’s also free to use the Mountbatten-Windsor name if required.
