This mouse (or rat) doesn't seem to have a name (he may have one, but we have yet to find out what). He is very kind to Unico, even though he's scared of him at first because he thinks Unico was a cat. The mouse has a long nose and tail and has brown colors with long whiskers.
The mouse, being a parent himself, feels sorry for Unico and gives him food from his sack, even though it seems that food is becoming scarce where he lives and when he doesn't even have enough to feed his own family in the first place. He helps Unico further when he finds out he doesn't have a home and introduces him to Chiko, hoping that Unico can stay with her. He also explains to Unico about Chiko's illness.
The mouse seems to be very concerned about Chiko's diminishing health because she's a sweet child he cares about too, and being a father, he obviously knows what it will be like for Ojisan if Chiko dies. He is often in Chiko's room watching her with his kids with worry.
