Think hard about the style of book club you are trying to name, whether it's a focused book club or one focused on romance, horror books, spiritual guides, or any of the plethora of other possible book topics out there. If you live in a town called Ridgedale and your book club revolves around romance novels, you might want to consider naming your book club "Ridgedale Romantics Book Club." That will give potential members an idea of what kind of club they'd be joining. If your book club focuses on books in general, you might want to name your book club something merely related to the area the book club is based. In that case, you might want to consider calling the club "Ridgedale Book Lovers."
Say the name of your book club out loud to yourself (once you have a solid idea in your head for a name). Say you picked "Ridgedale Romantics." Think about whether you like how the name sounds and whether it sounds like a book club you'd join if you saw a listing for it somewhere. Make sure it intrigues you and sounds unique and interesting.
Consult the members of the club and your friends. Find out if they like the name. Ask them if it sounds like something that would interest them and make them want to learn about the club. If so, then, success! You've just created a great name for your book club. Go on, start reading now!