We do mostly small animals which are poultry (chickens, ducks, geese, turkeys), rabbits, goats, dogs, we also have one kid that does llama's and one that might do pigs. The kids are do crafts also. There are about 35 clubs in our county, several are horse clubs, some do just crafts, some do just a variety like ours. Some have names from their particular areas, some from their interests, some are just country type names, some I have no idea what they mean or where they came from.
One the kids have thought of is "Hens, Hounds and Hares". Or "Hens, Hounds, Hares & ? (Honkers, Hammies, hillbillys???) this would give them 4H's like 4-H
I have also thought of "Fair Play" kind of a play on words.