I used to ride a mustang whose name was King too. It was a pretty good ranch horse and we made some good cowboying together. He had a strong mind and also a very strong heart. If your horse is the same, I may suggest "King of Hearts" as a show name.
End game. It doesn't directly connect to King, but in chess, end game refers to when u have to make a huge or rather big sacrifice in order to win, like give up your queen or something. I just think it's a cool name that's pretty unique and kinda relates to king.