What is the name of Miguel's great-grandmother?

Miguel’s great-grandmother is Mamá Coco.

Mamá Coco is the elderly woman at the center of Miguel’s family in Santa Cecilia. Her full name is Socorro Rivera, although the film most often identifies her by the affectionate nickname Mamá Coco. She is the daughter of Héctor and Mamá Imelda, making her Miguel’s great-grandmother.

Because Mamá Coco is elderly and frail, Miguel’s relatives worry about her fading memory. Her condition becomes crucial to the film’s supernatural rules: Héctor, her father, is in danger of disappearing from the Land of the Dead if Coco no longer remembers him.

The family initially treats Coco’s old memories as fragments of the past, but Miguel discovers that she still remembers her father. When he sings “Remember Me” to her, she joins in and later reveals the missing piece of the family photograph. Her memories restore Héctor’s place in the family story and help expose Ernesto’s theft.

Mamá Coco is not the same person as Abuelita Elena, Miguel’s grandmother, or Mamá Imelda, Coco’s mother. Those three generations are a common source of confusion.