The pets are very different to ukes. I would always name a pet, instead call him/her like fox terrier or siamese.
They respond to names and are personal beings dear to our hearts
I can understand names like Willie's Trigger for sure though. They can can get attached to a very special instrument when they get really special. I mean famous. Still they are inanimate objects. There is the difference.
Or late BB's Lucille. Though I quite sure there were many in that name lool.