For horses, you have to be riding them and then right-click with the name tag to use the it on them. I was just messing with naming stuff in creative, didn't know that they are going to be added to dungeon chests. That's pretty cool.
add parrots maybe? spawn in jungle biomes. You have to stand still and they will land on your shoulder. once that happens maybe you clip their wings with shears and they are tamed? with a few different colors like cats. Maybe they can be used to send messages to other people? Just my idea of another pet.