"Past precedent is that such surnames are dropped from usage in adulthood, after which either title alone, or Mountbatten-Windsor is used when necessary."
I remember reading years ago that Lord Mountbatten tried to persuade the Queen to change the royal name to Mountbatten but didn't succeed. Looks as if that was wrong, although he didn't altogether succeed if she would not drop the Windsor part of it. Or does the Government make these momentous decisions?
If normal precedent were followed, the Queen's descendants would be named Mountbatten, or Battenberg to give its original style. In the same manner the House of Hanover came to an end with the accession of Edward VII, being styled the House of Saxe-Coburg-Gotha, that of Prince Albert (later changed to Windsor during WWI). Both the late Lord Mountbatten and Prince Philip were upset when it was decided to continue the name of Windsor, the reasons for which have not been entirely clear.