Well, I'd like to see a name which has been well-used in England and/or Scotland since medieval times but has never made it to the throne, such as
Thomas,
Robert,
Roger,
Walter,
Adam,
Hugh, or
Geoffrey. For a less common alternative, how about
Eustace, the name of the son of
King Stephen who was disinherited from the throne because of the peace treaty naming the Plantagenets as
Stephen's heirs.
Eustace died before his father, but back then there were tales it was of a broken heart because his chance at being king was lost!
https://en.wikipedia.org/wiki/Eustace_IV,_Count_of_Boulogne