Not quite. The Liberal MPs are direct ancestors of the radical Whigs. They are wrong on many issues, but right here.
Charles Windsor Saxe-Coburg, private citizen, sounds good right now.
Their last name was changed by Royal Warrant to Windsor by Elizabeth II. And Charles's last name would have been Mountbatten anyhow, not Saxe-Coburg-Gotha (which was a title and not a last name). George VI would have been the last to have that title, but the family name was Wettin or perhaps Wipper until Eliz. II married Prince Philip.
I'd just as soon Charles wasn't king of anything (he strikes me as a rather dense and tone-deaf twit) but the English manage to get rid of the really stupid ones (see Edward VIII, the execrable Albert Victor, and so forth).