My boyfriend and I just went through this whole name deciding thing with my parents actually, for his daughter.
At first he was really possesive about it and didn't feel comfortable having her call them Grammy & Pappy or any for thereof...
I kept talking to him about it and laid it out as such... he said himself that he wanted my parents to be a part of his daughter's life. She is only three, so they will be around for most of her life... We plan on having children together, and I want all children to call them the same thing. I don't want the family to start off divided with one child calling them by their first names, and the other children calling them Grammy and such.
I had a long talk with my BF's Mom too, as her and I are close, and her family is a blended family, so I figured she could offer some insight. She agreed with me that my parents deserved grandparent names as they are already acting as grandparents (play with her, buy her things, all the grandparent-y things of spoiling, basically having a ball with it as this is the first grandchild in their lives, and my Mom has been wanting grandkids for sooo long). Her point was, either we are becoming a WHOLE family or we aren't... and the most healthy is to be a whole family and to stop sperating everything out... especially since Alex is so young and this is the family she will know for the majority of her life.
She talked to her son, and he came to the conclusion to ask my parents what they would be comfortable with her calling them. My parents were thrilled when I asked them, and without hesitation gave their answers! My Mom has always wanted to be Grammy... and to help differentiate (as both Alex's Mom's Mom and her Dad's Mom are Grammy), we tacked on the last name, Grammy Smith. My Dad said right away Poppy, which is not taken by anyone yet, so that works too.
So...talking to the grandparents about what name they would like is a good idea too.