Crono's Mom wakes him up the morning that he is transported through time. Crono was sleeping in, so his mother woke him up and shooed him out the door to have fun at the Millennial Fair.
After their journey through Heckran Cave, Crono and his party pay a visit to Crono's Mom in Truce. She is worried because she heard that he was arrested and sentenced to an execution. She's relieved that he's okay.
The party, without Crono, sees his Mom when they go to his house to retrieve the Crono Clone doll. They lie and tell her that Crono is doing just fine.
In the game, she is never given an actual name. When her dialogue boxes pop up, she is only listed as "Mom".