All pets, animals, and familiars in my game get names that I think the sims owning them would give them. For example, the farmer Mrs Blanchard loves the colour white, so her pets and farm animals are all white and have names that mean "white", such as Albus, Bianca, Whitney, and Shiro. A vampire named Mercury has a cat familiar named Sir Wednesday, because Wednesday is the day of the week that represents the planet Mercury.
Sometimes, when I don't have an idea, I just pick a random theme and go with it. In my secondary save, I have a coop of chickens named after heroines from popular book and movie franchises, and when Katniss and Hermione died (because I had forgotten to disable ageing for farm animals), their identical-looking successors were simply called Katniss II and Hermione II.
The only ones I don't name are wild rabbits because they come and go, and don't belong to my sims anyway. Another exception will be my planned Dungeon Keeper household, where the chickens only exist to produce food and no one has any friendly relationships with them.
