It'a definitely the sort of name the Collinses would have chosen. On the New England side of my family, I'm descended from a Barnabas, and I've got seven other Barnabases that I know of scattered through my family tree - stuff like "1st cousin 7 times removed".
I watched a couple of videos of Barnabas (drat, can't seem to copy the accent in) Kelemen playing Mozart. Very pretty, except he kept opening his mouth.