Lots of people keep mice as pets. There's are even mouse fanciers out there that breed for color, markings, and temperment.

Now mice aren't the smartest rodents out there but they can be tamed with constant patient handling. If you go slow they start to see you as safe ground and you can let them wander because they'll come back to you when scared. Mostly though they tolerate handling and petting but remain skittish.

I keep rats as pets and breeders and they make better pets because they are more easily trained but mice can be too with more work.

I also have mice.
I tame down all my mouse breeders so that I can handle my litters within a day of birth. But I haven't named them.... yet