While most male siblings share a surname and pass it on to their children, Prince William and Prince Harry's children do not share the same last name. According to Hello Magazine, William and Kate Middleton's children Prince George, 8, Princess Charlotte, 7, and Prince Louis, 4, all have the "Cambridge" for their last name. It comes from their father's title, the Duke of Cambridge.
According to the magazine, Prince George is enrolled as "George Cambridge" at his school Thomas's Battersea and his siblings are all known as Charlotte Cambridge and Louis Cambridge at school and at nursery, respectively. On the royal family's website, they explain, "People often ask whether members of the Royal Family have a surname, and, if so, what it is. Members of the Royal Family can be known both by the name of the Royal house, and by a surname, which are not always the same. And often they do not use a surname at all."
They also explain that in 1960 the Queen in Privy Council declared that male-line descendants of the monarch without royal titles shall take the name Mountbatten-Windsor, a nod to the Queen and the late Duke of Edinburgh.
When Harry and Meghan Markle's first child Archie was born in May 2019, Buckingham Palace announced that he had not been issued a royal title and instead would be known as Master Archie Harrison Mountbatten-Windsor. His younger sister Lilibet Diana, who just had her first visit to the royal palace, also uses the same surname.