I really like Ellays theory of naming your pets after each of your toons (as this method seems acceptable).
Yeah. How messed up is THAT policy, eh? Bizarre.

Do you (or anybody else reading this) know if Healbot is at least smart enough to differenciate between pets and owners with the same name? I'd hate to get a pet with the same name as its owner and find that only one of them showed up

That's pretty easy to test actually. I should probably get around to doing the pet quest on my level 27 hunters some time and give it a go....