I would love to be able to call it "__'s apprentice", for instance, my wizard name is Elizabeth, and I would love to have an option to call my pet "Elizabeth's Apprentice" cause it's my pet after all.
Or I would add some adjectives to the pet names like charming Bo, or dashing Jack, or marvelous Lola, magnificent Li, cheeky Ben, silly Billy and such. I feel it adds a lot of options and character to the pets.
Shmoopy - it's the name of one of our cats. Our other 2 cats are in the pet names :) But a Shmoopy would be awesome!
It's funny because my very first thought before any responses had posted was "Shmoopsey" very close to what the first response turned out to be :D I did ultimately change my mind to another name set, but this is funny to me.
A first name of Magnificent, or Incredible, even The Great, would be good. Failing that, how about Crusty? or Bozo? The names currently available are so generic. Buddy would even be better. Imperial, or Maestro, come to mind for titles, but Galahad, Arthur, and Fang, are good, as last names. Imperial Fang, of the North, sounds like a pet I'd buy, even if it be a butterfly. Genghis, or some other conqueror, or just Conqueror, also allow sobriquets such as "of the (north, south, east, west)". If the pet got larger, or changed in appearance, then names such as Baby, might not apply, but since the pets are born full grown, the names should reflect what they'll be at Epic status. The incredible Hulk, might not be available, but The incredible Thing, would work, in a pinch.