Never knew my grandfathers, but we called my grandmothers "Grandma". If we were referring to them when they were not there, we used Grandma Costa or Grandma LaPlaca. If you called Grandma Costa "nana" or "nanny", you got a bop on the head! I think it's because they called her mother that (my great grandma who died just before I was born).

I don't have kids (except for my birds and I refer to my mom as "Grammy" to them. ) but my cousin's kids call my aunt "Honey"! That's what she always called them when they were babies and they started calling her that back. . .pretty cute!

They may just eventually make up their own names so it might not matter what your folks want to be called!