Legal Question in Intellectual Property in California

You want to trademark the name. I highly suggest using an attorney if the group name is important to you.

As a Franchise Attorney I agree with the other attorney answer. You can't copyright the name of your group - you need to consider protecting it via trademark or service mark, depending on what the group does. The name must also be distinctive and not used by others in order to qualify for registration at the federal level, which affords strong, presumptive rights in all states. Consult with a good trademark or franchise attorney in your area for specific advice.

Mr. Franchise - Kevin B. Murphy, B.S., M.B.A., J.D.

Franchise Foundations, a Professional Corporation

To qualify for Federal registration, a trademark must be used in interstate commerce. You might want to book a few gigs in Reno or 'Vegas. Yours would probably be a service mark, which is a sub-set of trademark.