I don't name my female mice, they get numbers for tracking purposes, but I recently broke down and started calling my breeder male Max. I've only got the one so he rotates between 10 females... quite the ladies man..lol.
My rats are a slightly different story. I have two male rats only so that they have a cage mate when not with my females and they are definitely pets. Tame enough that I can open their tub and let them roam around on the floor while I do things. It's nice to know I won't loose them, I can't take credit for this, I adopted them from a rat lover who tamed them down for me.
My female rats have names but as still skittish because they came from petco. I had every intention of not getting attached but kept getting Female 1 rat mixed up with Female 1 mouse and had to name them. I don't think I'd be sad to see them fed off but they get treats and pets which is more than I can say my mice get. I've just had my first litters from these girls and am looking forward to holding back two girls for breeders. I want to see how tame I can make a rat I've handled since birth, *sigh* attachment here I come.
However rules apply. Bite me, cannibalize all your young, or fail to breed and you are gone.