Pistols name is Pistol so that is what I always showed him under. I know with some show circuits you have to register your horse to accrue points, Virginia Horse Show Association is one example. You only have to register the horse once but I think both the rider and the horse have to be members. I don't think there is a rule on the name either so you can pick whatever name you want. I geuss some people just like a fancy name?
W/ AQHA you have to show under what your horse is registered so Riley go's by his registered name and I have to go by Jennifer even though I NEVER go by that because he is registered to my full name. Had I known that I would have put Jenny on his papers......