I really don't like it when you get a pet with a name already. Why? Because sometimes there really silly. Like my blue cyclops is named King Abbey. I don't want to use my gold and rename my pet because I didn't get a chance to name him at the first place. I would like that when you get a pet from a drop you can name him any time when it is still in egg stage but when it hatches into baby you are immediately given a window to chose a name! If you close the window with out pressing accept for the name you have chosen it will give your pet a random name! But the window wont be given when you are in battle, in minigames and such when you have no time for that.
I agree. It's so irritating that whenever I get a pet, not only is it already named, but it has the most ridiculously absurd name like 'Sir Trixie' or 'Miss Spike'. When a child is born, it's not automatically born with a name that some random person chose, right? It's named by the parents, and technically we're the parents of our pets, so why can't they be nameless until we choose to give them a name?