Probably looking at some kind of update to the IRS... may just need to file a name change instead of starting all over with a new 501(c) 3 filing and transfer of funds and status between entities.
There has to be a CPA somewhere in the club to tell us, right?
However, there is possibly an easy way out. There was a provision to subdivide the club as necessary. You could continue under a subdivision(s) and still operate under the original name and filing. That much I do know.
Either way, it definitely requires approval by the officers and a quorum of members, assuming again that the original by-laws are still in place.
That would mean getting a current roster in order as suggested by Chia and getting the word out by all means available.