Uh, I'm pretty sure that many people have suggested this before me but well..
I have grown fond of my little Dragon hawk (now that I said it then it would also be nice if the dragon hawk could be a bit quicker because when hunting it is so slow that it can't even help) but it's hard to get that special feeling of owning something if it doesn't even have official name. It's a bit dull to just have, for example, have a badass Dragon hawk following you that's just called dragon hawk. By naming pets they could get more unique and if someone else has the same pet they would somehow differ from each other. How this could be carried out, well, there could be a code to name your pet. You know, when releasing a pet and all you write to the chat /releasepet and stuff.
There could also be some commands for example to send your pet kill that cursed fawn or to send your pet to pick up an item from the seabed where that damned turtle fell when you killed it. We all know how annoying it is to fetch it from there, don't even try to deny it.
When killing things would it be possible for pets to level up? You know, get stronger?
Here's just a couple of suggestions :D
