Oh, I thought you meant that one set of parents was designated Grandma/Grandpa, so the other one had to be Nana/Baba or something (using heterocentric assumptions for convenience). It's my position that I would get some choice in what I was called as grandmother, not that I could police anyone else's title. So if the kids suggested Nana and I didn't like that, I could ask to just be Grandma Surname or Grandma Forename, but I certainly couldn't take the Grandma title away from Grandma Inlawsurname.

We did have a separate title for my kids' stepgrandmother, but that was at her own very kind and sensible suggestion, to avoid confusing the children by using the same name for their dead grandmother as for their stepgrandmother.