Since a high school Latin class, I have been giving my pets Latin surnames, usually descriptive of the animal, but not always. (Disclaimer: I only got to take one semester of Latin, many years ago, so I could make embarrassing blunders without realizing it. With names, I just stick to a nice, simple, nominative case nouns, or, in Dicere's case, a simple infinitive.) After Charlie had kittens, I decided that feline surnames should be passed on from mother to children. It would not be practical to try to use the father's name as a family name, since the father is not always known (and one litter may have more than one father). Thus I decreed that Charlie's surname became the surname for her sons. This means that family names would have feminine endings. But if I do not know the mother's name (which usually I don't), then an assigned surname will have the same gender as the cat. I also like to at least have some Latinized version of the first name, so Toby became Tobias, Sydney is Sidneius, Charlie is Charla, etc.
Duncan broke the rules, when I decided he had to have a Celtic name. He was so fiesty in standing up to the dogs, and since his core color is brown, a name that means "brown warrior" seems most appropriate.
The triplets are surnamed Pesalba because the one trait they have in common is they all have white feet. (Their mom had white feet and a lot more of the white spotting gene than any of her children.) As best I can tell Pesalba is a Spanish name, but for me it's pes (foot) plus alba (white).
One of my favorite names that I came up with was for a pig that we had--dad was determined to name her Suzie Q., which he felt was the only name for a brood sow--I was willing to go along with this as long as we understood that Suzie Q. was short for Susanna Quinerius. Quinerius is a corruption of Quirinius, governor of Syria mentioned by Luke in his account of the Nativity--I was just trying to find something Latinate that started with a Q. You will note that the ending on Suzie's name is masculine--pigs don't have to follow the same rules as cats.
My dog Jim is actually James Boethius, so that we could call him Jimbo (though we never do). He, of course, was named for Kirk. If we're on a walk and happen across roadkill, I can say, "he's dead, Jim."