I think if they ever did something like this, they would probably have to do it for specific minions.

Minions like the Wolf Pup and Coeurl Kitten, yeah you could probably get away with those two Fido and Fluffy since they're little animals and most people name animals. But naming your Wind-up Tataru would be kind of weird because it's just a mini version of a character you already know who already has a name. Plus how would Tataru feel if you named her wind-up minion "MashAllPotatoes"?

To be honest, if we could name minions I would just name them all "Kallistra Junior" because that's the only good name. Don't @ me.