After fishing and not getting a nametag my server and I went and created a villager breeder and got some villagers with nametags and we were very happy! I went and renamed the nametag in the anvil and placed it on a horse with the name "Skelly" and all was great. Came back the next day the horse was no longer named. Tried a second time with a dog and named it "Rose" and the same thing happened the next day.