THat's funny... last year around this time (or maybe it was the beginning of the year??) I asked the exact same question. I ended up calling the club... get ready for this: The 3rd and 4th Grade Book Club. So pathetic, but I wanted a really cool name and since nothing lived up to it, I gave up.
I love the name, Flashlight Readers, but I got that idea from Scholastic, so I'm sure it's copyrighted. I wanted something like that-- that would show how much the kids loved to read. Maybe try opening it up to them?
PS: I've found with my group, that we usually are "talked out" about a book in one session and I think my attendance would drop if I did two meetings. *Unless the book was not read the entire way yet-- we've never had that circumstance.