Dog names

I once read a short story about a vicar who, when he was drunk, told stories about his previous life as a dog. He had a dog friend, and every night the two dogs would go roaming. The two dogs had names of course, names their humans had bestowed on them, but dogs have their own names, names they give themselves. These two dogs had named themselves Moon Chaser and Lion Hunter (or was it Moon Hunter and Lion Chaser?)

What name do you think your dog would call himself or herself, and why?

(and has anybody else ever read this story and remember the title or author?)