Have you asked Martin Carthy and Norma Waterson whether they'd mind? They might be tickled pink.

To me "Lincoln Tradition(s)" sounds more limiting than you say, I'd expect a group with that name to be only doing trad Lincoln songs (and Man Tran is rather a long way from Lincoln!). I don't know how much difference the name actually makes, though, especially if most people first hear you rather than see the name.