My folks used to have a cat named Bill. It was a stray that wandered into our yard, and stayed. My brother and folks always assumed the cat belonged to our neighbor, Billy (he didn't). So, it was "Bill's cat", and ultimately, Bill, when the neighbor moved away and the cat stayed.

My rabbit's name is a mis-spelling. I named him NOAA, after my agency, and the vet wrote "Noah" so that's sort of stuck.

Your foundling is adorable, by the way. That 3rd picture is just too much!!