Anna,
I imagine that it is different in various parts of the English speaking world, but in English speaking Canada you can use the family name to distinguish them when you are talking about them.
My mother's mother is my grandmother. She would be Grandma Smith and her husband Grandpa Smith.
My father's mother is also my grandmother. She would be Grandma Jones and her husband Grandpa Jones.
When we are talking to them in person, we just say Grandma or Grandpa.
If you have them all together in the same room then of course you could use their last names or their first names to adress them. Grandma Mary or Grandma Smith, Grandpa Henry, etc.