Junior's grandmother's name is given only as "Grandmother Spirit" in the book. I don't believe her first name is ever mentioned. Junior speaks about his grandmother at length in two places in the narrative, and he addresses her only as "Grandma" or "my grandmother" (Chapters 9, 22, and 23).
When Junior's grandmother dies, a heretofore unknown anthropologist attends her wake. He has what he describes as a genuine Indian dance outfit, and says he has come to return it to its rightful owner, "Grandmother Spirit". Junior's mother identifies herself to him as "Grandmother Spirit's only daughter", and tells him that he must be mistaken. Grandmother Spirit was never a powwow dancer, and the outfit itself turns out not to belong to the Spokane tribe at all (Chapter 23).
Junior is very close to Grandmother Spirit, and has great respect for her. When he is at a loss as to how to respond to the treatment he is receiving at the white school he has chosen to attend, he goes to her for advice (Chapter 9), and he admires her especially because of all the people he has ever known, she is the most tolerant. In life, she accepted everyone as equal, even "weird people". On her deathbed, her dying wish is that the drunk driver that hit her be forgiven (Chapter 22). Grandmother Spirit very clearly had an enormous impact on Junior Spirit's life.