There is a bug, that if a pet gets renamed, the pet gets cloned somewhere in the world under the old name. It just sits there until it gets poked by someone with the proper poking stick. That's why you see some pets thrown about the world that seem to stay there for hours and hours.
At least, that's what I was told when I asked a month or so back. Not sure if this is still an ongoing bug, but from what you describe, I'm betting it is.