Having been in a variety of organizations, I know that it can be difficult, to say the least, when some one or two are not with the group. The name is often a bone of contention, & shows with whom the group will often have problems in coming to aggrements.
    These days people think of a variety of things when a specific word is mentioned. If the founding members are a small group, and one is never going to be happy with "club" the person should be able to compromise. Sometimes if they refuse to compromise it is because they have a specific idea & will never be happy till they get it, & or likewise never be happy & always resent it. If the person is reasonble, then suggest only 3 or 4 of the best suggestions the group of founders can come up with & vote on it.
Recently, I assisted a friend establish a program which was all about "Traditional American Music." This in itself can mean 10 different things to 10 different people. However, I wrote a long list of words of similar meaning, and some words which were quite out there--you never know what will spur you brain to think of just the right thing. Will all the Music be "Folk?" Make a list of works for "Folk" and a list of words instead of "club" & use an online thesarus if needed. From that list, I made a list of potential names & narrowed it down to a few & gave it to my friend. She loved them all, but chose the one which made the most sense for her goal.
For what it's worth, "Society" is a bit less exclusive sounding than "club." What is the end goal? An open mike? A a regular jam?
Weekly or monthly? Business meeting then Jam? Business meeting, informal learning workshops for the various instruments led by members followed by jam?


For example:
Folk Music Club==
Folk:
Acoustic
Traditional
Folkroots
etc.

Club:
Society
Association
Guild
Circle
Lovers
Jamtime
etc.

   
          Good Luck, and may your organization be a fun & happy one!