Considering that Catherine "Kate" Middleton is the wife of Prince William, it seems like she should be known as “Princess Kate” or “Princess Catherine.” After all, when Lady Diana Spencer married Prince Charles, she became “Princess Diana.” Right?
Actually, as Insider explains, it’s a little more complicated than that. In order to have “Prince” or “Princess” officially precede your name, you typically must have been born a prince or princess; i.e. descended from a monarch. Prince Andrew’s daughters, for example, are “Princess Beatrice” and “Princess Eugenie” because Queen Elizabeth II is their grandmother.
If you, like Kate Middleton, married a British prince, you’d take on the feminine counterpart to his official title. Though Prince William is called “Prince William” because he’s Queen Elizabeth II’s grandson, his official title is the Duke of Cambridge (among others). So, Kate Middleton is the Duchess of Cambridge.
Assuming that William’s father, Prince Charles, eventually becomes king, William will likely inherit Charles’s current title: Prince of Wales. But even when that happens, and Kate becomes the Princess of Wales, it would still be technically incorrect for us to call her “Princess Catherine.” Traditionally, when a woman becomes a princess because her husband’s a prince, she only gets to be called “Princess” if it precedes her husband’s name. So Kate Middleton would be “Princess William of Wales.” It’s not a very common practice these days, but it does still exist. The wife of Queen Elizabeth II’s first cousin Prince Michael of Kent, for instance, goes by Princess Michael of Kent.
In that case, was it incorrect to call Diana, Princess of Wales—who was not a born royal—“Princess Diana”? Yes. But the moniker was so widely embraced by the media and the public that people paid little to no attention to its inaccuracy.
Also, the royal family has broken protocol plenty of times in the past, and they have the power to bestow atypical titles as they see fit. Having descended from both Greek and Danish royalty, Prince Philip had already technically been a prince since birth—but in 1957, as Town & Country reports, Queen Elizabeth II named him “a Prince of the United Kingdom of Great Britain and Northern Ireland, Whitehall.” From then on, he was officially “Prince Philip” in the UK. Why he was never “King Philip” is a whole other matter.