Multiple Grandpas over here, one was "Grandpa", the other was forename only unless old-fogies yelled at us for being disrespectful making him "Grandpa Richard". One grandmother was forename only but interestingly old-fogies didn't yell at us about that. Other Gran was "GranGran" cos she wanted to be 'GanGan' like Queen Victoria and my sister oldest grandchild mangled it. Stepgrandmothers (both married to Richard) did NOT get a grandma title, they were just forename and I think would have shouted at us for anything else (weirdly upper class enough not to actually follow the convention with children and manners).
My nieces get Grandpa+Forename for their biological and stepgrandfathers and while there is now only one left, I suspect that'll stick due to how they're talked-about to them rather than becoming just grandpa. The grandmothers vary with a Nana (now dead), Grannie (my mum, alive and kicking arse) and Grandma (Gail, stepmother to sister and me - I think if my sister could ungrandma her title wise, she would
).
You can probably have a name you choose and the children or family will end up with a different name entirely.
