Can I do it, and if I can, HOW? ")

You can indeed with an Enchanted Hypnosis Wand. :)

It's a one-use item that you can buy with sp from another user or from the Cash Shop.

To change your Pets name you need this item:

[item2=Enchanted Hypnosis Wand]

You can buy it for 1000 CSC from the cashshop or from other users.