I love it when they choose themselves. I refer to myself as Grandma, but eldest gd and eldest gs, are cousins and spent a lot of time together in their early years both called me Mumma for a few years, now they call me Grandma. Third grandchild called me Ahma but now he is three he calls me Grandma. Fourth grandchild also three calls me GRuumma, I think its the way she speaks. Youngest grandson also three has always called me Grandma. He also calls my mother Old Grandma while my other grandchildren call her Great Grandma. Their other grandparents range from Grandma, nanny, nana, papa, granddad and maybe a pop. It doesn't seem to matter, if they are referring to another grandmother they might say Grandma and then her first name.
Middle grandson was cross when his mother asked him if he knew that Grandma had another name. As far as he is concerned my only name is Grandma and that's it. 