The British Royal Family
Their Last Name
The royal family has little use for last names - after all, everyone knows who they are. Princess Diana did not take back her maiden name, Spencer, after her divorce; she continued to be known simply as "Diana." The queen signs official documents "Elizabeth R." The R stands for Regina, which means "queen." (Regina is not one of her given names; she was baptised Elizabeth Alexandra Mary.)
But the royal family does have a last name, and they do use it from time to time. This wasn't always the case. Queen Victoria's husband, Prince Albert, was a member of the House of Saxe-Coburg-Gotha, so her descendants were part of that dynasty. This, however, was not the family's last name. They didn't have one, because they didn't need one, so they didn't worry about it. Experts later worried about it for them and decided their name was probably "Witten" (or maybe even Wipper).
The royal family's official name, or lack thereof, became a problem during World War I, when people began to mutter that Saxe-Coburg-Gotha sounded far too German. King George V and his family needed a new, English-sounding name. After considering every possible name, from Plantagenet to Tudor-Stuart to simply England, the king and his advisors chose the name Windsor.
To this day, the British royal family is known as the House of Windsor. When Princess Elizabeth (the current queen) served as a subaltern in the Auxiliary Territorial Service during World War II, she was called "Elizabeth Windsor." Elizabeth married Prince Philip of Greece, whose family name was Mountbatten, and eventually she decreed that most of her descendants would be called Mountbatten-Windsor. Princess Anne used this name in 1973 when she married Captain Mark Phillips.
However, according to statements made by the queen, it appears that Windsor is still the official family name for any British royal who is styled "Royal Highness." The queen's youngest son, Prince Edward, the Earl of Wessex, has used the name Edward Windsor professionally. His wife calls herself Sophie Wessex.