An article on www.carstairs.org.uk/carstairs/history/intro.htm
parallels a theory that I advancd on the origin of "Carwall" if not "Caldwell".
It says that the vilage of Carstairs was originally Castel-tarris and became Carstairs through the celtic word "Caer" for fort.
Castle-Wallace (modern spelling) might have been spelled in earlier times Castel-Wallys then Carwalls. The farms of Castlewalls near Walls Hill seem to confirm my thoughts.

... but I still can't make well-known and accepted Scots "nickname" Carwall unto Caldwell. I can see how it might go the other way Caldwell->Carwall but that doesn't fit the Castle-Wallys theory which would have to come first.

I would welcome some thoughts from any "deep thinker" - I think I am close but that final connection Carwall->Caldwell in that order eludes me.