Hi K,
I think the answer is Yes and No. I am a lab owner and so if I was going to buy something in lab form, if it was already named I would not personally purchase it, it would take away the personal centiment I would have wanted in purchasing it. And no if you do not own a pet, and just like the sweet storyline, and adorable new friend.
My suggestion, keep the story line and add something to the affect of, all this little guy is in need of is a good name and good home. etc. I'm no pro.. just my two cents.. love your items!!