Mountbatten-Windsor is the personal surname used by some of the male-line descendants of Queen Elizabeth II and Prince Philip, Duke of Edinburgh. Under a declaration made in Privy Council on February 8, 1960, the name Mountbatten-Windsor applies to male-line descendants of the Queen without royal styles and titles. Individuals with royal styles do not usually use a surname, but some descendants of the Queen with royal styles have used Mountbatten-Windsor when a surname was required.
The British monarchy asserts that the name Mountbatten-Windsor is used by members of the Royal Family who do not have a surname, when a surname is required. For example, Prince Andrew, Duke of York, and Anne, Princess Royal, children of the Queen, used the surname Mountbatten-Windsor in official marriage registry entries in 1986 and 1973 respectively. Likewise, Prince William, Duke of Cambridge, used the name when filing a French lawsuit related to the topless pictures of his wife published by the French magazine Closer.
At the time of the 1960 declaration, palace officials claimed in private communications that it created a hidden surname that would emerge several generations later when some of Queen Elizabeth II’s descendants were further removed from the throne. On the wedding of Prince Edward and Sophie Rhys-Jones in 1999, the Queen decided, with their agreement, that any children they might have should not be styled His or Her Royal Highness. Consequently, the birth of their daughter in 2003 marked the first emergence of the Mountbatten-Windsor surname. Their daughter was named Louise Alice Elizabeth Mary Mountbatten-Windsor, although she goes by the courtesy title of Lady Louise Windsor, her father being the Earl of Wessex.
Mountbatten-Windsor differs from the official name of the British royal family, which remains the House of Windsor. In accordance with law and custom in the English-speaking world, the surname Mountbatten-Windsor belongs to all male-line descendants of Queen Elizabeth II and Prince Philip, and is used by them if and when a surname is needed. Other descendants of King George V, the first monarch of the House of Windsor, use Windsor as their surname if and when a surname is needed: for example, descendants of the King’s sons Prince Henry, Duke of Gloucester, and Prince George, Duke of Kent. The King’s other two sons, King Edward VIII and Prince John, left no descendants.
Archie Harrison Mountbatten-Windsor is the son of the Duke and Duchess of Sussex, and is the first descendant of the Queen and the Duke of Edinburgh to use the Mountbatten-Windsor surname.
A great-grandchild of Queen Elizabeth II, Archie Mountbatten-Windsor is seventh in the line of succession to the British throne. He is also heir apparent to his father’s Dukedom of Sussex, Earldom of Dumbarton, and Barony of Kilkeel.
Under the terms of the Letters Patent issued by King George V in 1917 – the sons and daughters of sovereigns and the male-line grandchildren of sovereigns are entitled to the title of Princes/Princess with the style of Royal Highness. The Letters Patent in 1917 also included the eldest son of the eldest living son of the Prince of Wales – but was amended by Letters Patent by Queen Elizabeth II in 2012 prior to the birth of Prince George of Cambridge so that all the children of the eldest living son of the Prince of Wales would bear royal rank.
As The Duke of Sussex is not the eldest son of the Prince of Wales, his son is neither a British prince nor does he have the style Royal Highness, which is the gift of the Queen (usually acting on the wishes of the child’s parents). There was the option of using Prince Harry’s subsidiary title of Earl of Dumbarton, as a courtesy, but Meghan and Harry decided instead that he would be styled as Master Archie Mountbatten-Windsor, in accordance with their wish that he grow up as a private citizen.
When the Prince of Wales becomes King, Archie then will become the grandson of the sovereign and he will technically be entitled to the title of Prince with the style of Royal Highness. However, the Prince of Wales has stated the desire to trim down the number of working members of the Royal Family, and with the desire that Archie grow up as a private citizen, his obtaining the style and title is highly unlikely. I suspect a new set of Letters Patent once the Prince of Wales becomes King, replacing the 1917 Letters Patent.