So much depends on the child. My mother's mother wanted to be called Grandmother or Grandmama. Well, my oldest sister called her "Mama" and since she was the cutest little girl in the world according to my grandmother, she became "Mama". All three of us called her that. But my cousins called her "Grandmother".
My mother was Grandmama to my kids because that is what the cousins called her and my dad was "Granddaddy". We lived 1300 miles away so when they were learning to talk the grandparents were not around. They called my in-laws "Grandma" and "Grandpa" because that is what they wanted to be called.