It's complicated.
The Queen has stipulated that all her male descendants who do not bear the titular dignity of Prince shall use Mountbatten-Windsor as their surname.
Willam and Harry, though, DO "bear the titular dignity of Prince".
For these cases, children generally use "Prince X of Y" where X is their given name and Y is their father's territorial designation. For William and Harry, their father is Prince Charles, who is the Prince of Wales, so they were "Prince William of Wales" and "Prince Harry of Wales".
This is normally dropped when such children reach adulthood and simply use their title. You need a last name when you might get confused with someone else. The likelihood of, say, Prince William, Duke of Cambridge getting confused with some other Prince William, Duke of Cambridge is pretty small.
However: William and Harry were both in the military, and not having a surname in the military is a little awkward. Both of them used "Wales" as their surname in a military context. William (as Duke of Cambridge) now has his own territorial designation; I'm not sure if he's been updated officially to "William Cambridge" in the military or not.
Mountbatten-Windsor
Prince Harry was born September 15, 1984. Prince William was born June 21, 1982.
Most likely Windsor as that is the surname of Prince William, but I am not sure.
William Wales
Windsor is their surname. Their titles will be Prince and Princess of Wales.
Harry Styles
Prince William has various surnames available to him, including 'Wales', 'Cambridge' and 'Mountbatten-Windsor'. The surname a royal uses (if they use one at all) tends to reflect their title.
His father is HRH The Prince of Wales, so Prince William takes the surname 'Wales'The Royal Family don't tend to use surnames unless one is required by custom, in which case a surname is used based on the person's title or family.Prince William can use the surname 'Wales' (due to his parents being the Prince and Princess of Wales) or 'Cambridge' (as he is the duke of Cambridge) or 'Mountbatten-Windsor' (which is his family name).
prince harrys godfather is Gerald Ward
BrowN
Styles :) x
Prince Henry Charles Albert David