Being single, I'm not a grandmother and never will be, but we called out mother's mother Granny (and mum is called Granny by her grandkids) , and dad's mother was grandma or grandmother. Both grandfathers were grandad. I think (personal opinion only!) that Nana sounds like a goat (they probably have grand-kids, so that's OK)!! Nanny sounds like an employee hired to look after children.
I'm very glad I'll never have that decision! Janet