I dont think that it possible 
Dominator pets are just like the Hero Controller ones. As far as i am aware
un-nameable. and always on follow/agressive
@Inkwave ..(darn merge)
Thats true from what I have seen too
And thats exactly how it should be. Controller pets are "summoned". They are nameless entities that are entirely generic they posses very limited intelligence and basically just follow and kill.
Mastermind henchmen are different, they are at least semi-intelligent individuals who work for you. They are effectively the same minions each time you call them. They follow orders and can be used much more tactically.
Can you name pets like masterminds or not?