This minor character having a proper name helps to reinforce parallels between Chrono Trigger and it’s sequel, Chrono Cross. Both open with the main character waking up and being greeted by their respective mother. But unlike her counterpart in the American translation of Chrono Trigger, the mother in Chrono Cross has a name: Marge.
I wonder what impulse prompted whoever translated the first game for English-speaking audiences to simply call the mother Mom. Did they think American players wouldn’t get who this strange woman traipsing into a young man’s bedroom would be? Did they think we couldn’t wrap our heads around the notion of a mother having a name other than Mom? It’s an odd choice that presumably was made for some reason. Otherwise why make it?