Thanks to the lucky folks who married into royalty like Diana Frances or Kate Middleton we know the British Royal Family must have a last name, but many are unclear as to what that last name is.
We know it must be something other than "of Wales" or "of York", but as a rule the Royals don't use last names except for times when they must, such as when they're in school or in the military.
So what's the deal with the royal last name?
Prior to 1917 members of the British Royal Family didn't use "common" last names at all, instead using their first name with the name of the house or dynasty they're part of, such as the House of Tudor or House of Wales.
But in 1917 King George V changed his house name from Saxe-Coburg-Gotha to Windsor, a name derived from Windsor Castle which was changed due to anti-German sentiment.
George V not only changed the dynasty name- he made Windsor the royal family's surname, thereby doing away with any common last names.
To make matters more complicated Princess Elizabeth made another Royal Family name change when she married Philip Mountbatten and became Queen Elizabeth II, declaring the last name to be Mountbatten-Windsor.
So now descendents of the Mountbatten-Windsors can use Windsor, Mountbatten-Windsor, or if they have a title such as "His Royal Highness Prince" or "Her Royal Highness Princess" they don't have to use a surname at all. Now it's all so clear! *wink*
Read Here's Why The British Royal Family Doesn't Use A Last Name here