Tora Ziyal wrote:
Except they do have a last name. They just don't use it much. (See quote and link in message #106.)
While that's true (and I think Mountbatten-Windsor is a super cool name), none of the royals seem to use that in public usage. As mentioned, Harry and William used Wales, and their cousins Beatrice and Eugenie use "York" as a last name at school. I think Charles and Andrew used Windsor when they were in school, or at least I remember reading that somewhere.
"Mountbatten-Windsor" is a really weird concept. It's not really their legal name (like on passports and stuff), but they can use it if they need to. I don't pretend to know how they use it or would use it in day to day life, but as far as their legal name is concerned, that's not part of it.