I'm sure it is quite common. I had a lot of stuffed animals as a kid, and most of them were dogs. Their names had one of these two sources: a "child-ified" version of their breed name (my stuffed dog resembling a German shepherd was named Sheppy), or randomly borrowing the name of a famous dog from a movie (example: I had a stuffed dog named Benji who bore no resemblance to the character of the same name). Non-dog animals had more arbitrary names, usually after their physical characteristics or life histories I made up for them. And all of my stuffed animals had the same last name as me, like Sheppy [my last name] and Benji [my last name].
So yes, it's definitely common to have a naming scheme for one's stuffed animals. My friends had a naming scheme in place too (one friend used the dominant color of the animal with a Y added to the end), although I was the only one who used a last name. It's perfectly normal, for aspies or NTs. Perhaps the tendency dates back to Adam and Eve being told to name the animals they find in the Garden of Eden if you're religious, or the natural human desire to give a scientific order to the natural world around them if you're not religious.