Magia
Connection
Equilibrium
Miracle 

LEGIT TAKING WORDS FROM A DICTIONARY. I like Reincarnation. It sounds pretty cool.

Though for pets, I'd rather that we can all use pets but all to varying degrees. Like a thief not being able to command a Lion Beast as well as a Beast Tamer. So the drawback is on the class not on the pet. Mounts can be used when needed and such. Also for say a magician to use a Phoenix Lizard to it's full potential they need certain equipment and such.