Firstly, the names of the pet levels are fine except for Epic, Mega, and Ultra. These make no sense, especially since they are not named after eras of life like the first 4. I believe Wizard101 should continue the pattern of naming pet levels after eras of life. I have some suggestions.
Baby does not get renamed. Teen gets renamed to Kid. Adult gets renamed to Teen. Ancient gets renamed to Young Adult (hatching can start here). Epic gets renamed to Adult. Mega gets renamed to Elder. Ultra gets renamed to Ancient.
Secondly, there should be more pet training variety besides Grub Guardian & boring pet games. Pet training should be fun. Grub Guardian is fun, but I'm not always in the mood for it, and you can get sick of the game, which is why I took a hiatus from it. So, more ways to train pets would be good, including on Pirate101 (they have pets if I recall correctly, but not positive). KingsIsle can try to incorporate other games of theirs into pet training like their Rise & Destroy app where monsters destroy cities like Godzilla. With Rise & Destroy, the monsters needn't be the pets. You can choose, before entering the game, which pet to train, and the monsters can simply act as proxies for the pet.