My dad's name doesn't 'go' with any of the names we like, and neither DH nor I like his name at all. It also doesn't go with our surname.
It's not family tradition per se but I like the abstract idea of using a family name... if only it was a name I actually liked!
My dad had a pretty awful family unfortunately. I actually like his dad's name, but he was an abusive alcoholic so we're certainly not going to use that!
I think we might just have to go with the non-family name that we like.