In the Rievaulx Cartulary of 1154 - 63, Dowthwaite was ‘Duvanesthwat’, derived from the Old Irish Dubhan (in turn, derived from dubh gail - 'black foreigner', usually applied to a Dane).
The Duffin Stone probably gets its name from Dubhan, too. Unlikely in this area before c.10th. a.d. The stone is, of course, much earlier.