the name of the club is no longer "Chicago Croquet Club". I bought a
croquet book today at Borders and in the back it has a listing of
croquet clubs in the U.S. There's one in Park Forest, IL with that
name.

I say, instead, we simply go with "Chicago Croquet".

Other ideas are:
Chicago Croquet Circle
Chicago Croquet Coalition
Chicago Croquet Confederation
Chicago Croquet Corps
Chicago Croquet Cooperative
Chicago Croquet Conspiracy
Chicago Croquet Colleagueship
Chicago Croquet Coadjuvancy
Chicago Croquet Association
Chicago Croquet Allliance

~matt