When we don't want our dog to get excited about talking to/about him, we call him the Canine Unit and we have to spell (he is a super intelligent Golden Retriever--smartest dog I've ever had). "Did you f-e-e-d the Canine Unit tonight?" Pup, Pupper, Pupster, Brat, Pest, Boy, Mutt, Hairy Wonder. His name is Reilly , so sometimes we call him "Rei Guy".
We don't have cats, so they don't get referred to collectively very often.
Growing up on a farmette, we had cats, and they were always "the cats" or referred to by name. Miss Kitty, Punch and Judy, Gabe, and Missy were their names. We had a horse and she was always called by name or Pretty Girl or Beautiful Beast.