I'd like to find out whether a pet name I have in mind is taken or not. Is there a way to do this other than attempting to create and name it?

You can add the search widget to your sidebar from here c:
Or you could fill the pet name into this url: http://subeta.net/pets/PETNAMEHERE

I prefer the search though because even if the name is on an active account, you'll get any names that contain the search term and some of those might be available, or might trigger an alternative idea for you c:

Thanks! That answered my question.