Royal people don’t generally use surnames in the sense that we’re used to. Will has a bunch of given names (William Arthur Philip Louis) and some titles, but that’s all.
Where a surname is needed, the place associated with a title is sometimes used. (So Cambridge in Will’s case.) His father Prince Charles (Prince of Wales) sometimes uses Wales as a surname, as did the late Princess Diana.
Windsor is the name of the royal house, but that’s not really a personal name. It’s just a label for the current dynasty.
Some military uniforms require a name badge/tag. It could be plastic, metal or cloth. I believe both William and Harry wear one that says “Wales” when required. That being said, in 1960, Queen Elizabeth had declared that her offsprings’ last names would be “Montbatten-Windsor” in situations where they needed a surname.
It sort of depends on how they’re addressed too. If their honorific is used, no last name is used. Example: His Royal Highness, William, Duke of Cambridge.
Both William and Harry use Wales as a surname when they need one. William was enrolled in college as William Wales, and was William Wales in the Royal Air Force (where his nickname was “Billy the Fish”). Prince Harry is known as Captain Harry Wales in the military.
Elizabeth R = Elizabeth Regina (i.e., Queen Elizabeth).
For male monarchs, R stands for Rex (king).
The Prince of Wales usually signs as Charles P (Charles Princeps = Prince Charles).
Victoria signed as Victoria RI (Victoria Regina Imperatrix = Queen-Empress).
“The Cambridges” is just journalistic shorthand for people who don’t have a true surname. “The Windsors” would be both incorrect and indeterminate, as lots of people in the royal family could be the intended subject.
You mean she uses “R” even when it’s not Talk-Like-a-Pirate Day? It’s actually more like signing it as a short form of Elizabeth II, Dei Gratia Magnae Britanniae, Hiberniae et terrarum transmarinarum quae in ditione sunt Britannica Regina, Fidei Defensor.
He specifically chose to retain “Wales” as his placeholder surname instead of switching to “Cambridge” after he got married (& was made a duke). His uncle, Prince Andrew, on the other hand went from being Lt. Windsor to Lt. York on his marriage (& being made Duke of York).
Right, remember the War of the Waleses? The same shorthand can be used to describe any peerage couple not just royals.