The Beverley branch is so called because many of its members lived in or around Beverley, East Yorkshire, during the second half of the 19th century. They don't seem to have originated there, having moved around extensively (gee, thanks guys), but Beverley does serve as a convenient reference point for them.
There are descendants still living in and around Beverley today, with others in West Yorkshire from a sub-branch that moved to Harrogate.
To become a member yourself, contact the co-ordinator. Don't worry, it's free!