In theory we are free to do it now. New Zealand and other "old" Commonwealth countries (Australia and Canada) have now evolved to independent countries that has its own laws governing monarch succession, and the only constitution ties with Britain itself is that we share the same current monarch of the United Kingdom.
If we so choose, we can actually call in a completely different royal family as our constitutional monarch, but I suspect if we ditch the House of Windsor (not Mountbatten-Windsor as some have claimed) as our royal family, most of us to choose to go republic altogether.
Hey, it's time for some new blood! It's not all their fault, but they've gotten stale and overexposed.
Isn't that really the House of Hanover? During World War I it was rather awkward for the royal family of Great Britain to have a German name when Britain was at war with Germany.
NOTES: Christened: Albert Edward; called, "The Peacemaker" Reign: 1901-1910; It is not always realized that Queen Victoria was the last sovereign of the House of Hanover and King Edward VII was the first of the House of Wettin or the House of Saxony. Edward VII, in an outburst of anti-German feeling engendered by the First World War, changed the name of his "House and Family" from Wettin to Windsor in 1917. Edward gave his name to the Edwardian period.
Don't think that's correct.
" . . . at present it is virtually impossible to be sure whether the Royal name is Windsor or Mountbatten-Windsor. . . "
- Debrett's. That's the last word on this sort of stuff, like the Almanach de Gotha for the Krauts.