When we were children we called our grandparents Grandma Smith and Grandma Jones. When my sister moved out west, her mother-in-law was living nearby. So she went by Grandma Eileen and the Great Grandma went by Grandma Ellie. When I had Grandchildren, I wanted to be called Grandma Mavis. My children had a problem with that at first, but I always signed my cards Grandma Mavis, so it caught on.
Using your first name helps the children keep the grandparents straight when they talk about past generations.