I never knew there was a 'rule'. Growing up we called my mothers mother nana and my father's mother nanny. I only had one 'poppy'. Never called either grandma or grandpa.
When my kids were born we asked our mothers what their preference was. DH's mum is nana (his father grandad) and my mum is nanny (my dad is poppy). My mum also made the comment she wasn't old enough to be a 'grandma' and that 'nanny' sounded younger.
I think it's perfectly reasonable for a grandparent to have a say in what they're called. However if the child calls them something else that's the child's call!