I call my mother "Mama". If I'm talking to someone else I refer to her as Mom or "my mother". My son called me Mommy when he was little. Now he calls me Mom. My sister's children are grown and still call her Mama. She said she never felt like "Mom" but "Mama". Oddly I never felt like "Mama".
I have no grandchildren. I will let my son decide what they call me when and if he has children. He called MIL "Grandmama". My mother is known as Grandmother, thanks to my father's formal family. My grandmothers were "Grandmother" and "Granny".
I would prefer Grandma, Granny or Grandmama over Grandmother or Mimi or Gigi.