I find it ironic one would name their dog, "dog" or Inu... Not a BAD irony, just a funny one. Its even more funny if they KNOW Inu means dog. Thats an owner I'd assume has a great sense of humor!
There was a guy in our neighborhood who had a Shiba Inu (we knew him only because we both had Shiba Inus) and he named it Shiba, which I thought was unoriginal, but hey... to each is own. Then again, my buddy growning up had a German Sheppherd that they named Shiba, and I thought it was great name for the dog.
I like naming my pets after something that FITS them. Usually I wait a little while to name them until I know them... Like our Shiba Inu we named Autumn because she would chase leaves with a voracious obsession. It wasn't healthy, but it sure was cute!
Then a cat named Tie because he looks like a Tiger - I admit, its not original.
A dog named Ralph, because when he barked it sounded like he said "Ralph!"
A cat named Adolf because he had a bad temper and a little black spot on top center of his mouth... He looked like Adolf Hitler and he ACTED like him too... loved that cat, but he was a little sh**.
And of course my best fish ever named DEETER, who was named after a character in a book that I read because of his personality.
YES I just said my fish had personality. What of it, huh?! jk lol
Anyways, therefore I've named animals after characters in history or books, but so far nothing form Inuyasha, and IF I ever do (and not planning on any new pets for a LONG while) then it will have more to do with the name FITTING rather than being simply because it was an Inuyasha name.