For me it depends... Pets get mostly named after something they're related to my farmers background or simply what vibes they send out, like Cloud for a white cat or Midnight for a black one.
Other animals like cows, chicken, ducks, sheep, goats, ostrichs, who are somehow always female, often get paired names like Pam & Sam or something connected with the sounds they make like Chatterine for a duck or so... Pigs and rabbits can be both genders, which you don't know before they're sended off to their new home, so I often end up with boys named Sue

And dinosaurs are named after somewhat dinosaur related like Nessie or so.