My son was the first grandchild. We had tried to come up with what Momma wanted to be called by him, but she just really couldn't do it. I think the fact that she was so young had something to do with that. Then a friend of the family told us that our son would pick out what he wanted to call her anyway, so it didn't matter what we wanted to call her.* We lived to regret letting my son pick the name.
He decided to call his gramma "Maw"! (Until he was about three, I always had a hard time trying to figure out if he wanted to go to the mall or to see his gramma!) Oh is was pretty horrible, but we all accepted it and went on with life. Then my sister's kids started coming along. Her daughter also called Momma, Maw -- for a while, until she was about three, I think. Or maybe it was four or five. Anyway, that was when we had a big family gathering at our place and our cousins Sundey, Kelly and Molly came with lots of other cousins, aunts and uncles. Kelly and Molly are twins and a few years older than my niece. This was the first time my niece had met most of the family in person because they had lived out of state. She was thrilled by the other girls and before the day was over she had started calling Maw, Mawlie. It wasn't long until the name changed into Mollie. Maw never fit Momma anyway and Mollie is so much prettier. I like it. Of course my son didn't stop calling her Maw. So, for years, whenever we got a card from Momma, it was signed Maw, Mawlie, Mollie and Mom. What a hoot! She wanted to make sure all those bases were covered.
We had the same problem of what to call her when the great-grandchildren started to roll in. My daughter-in-law thought that Mollie sounded disrespectful for a great-grandchild to call her great-grandmother. So, after some discussion with both my Momma and my daughter-in-law we decided on Granmollie.
*We learned that that statement was a bunch of mule muffins! I child will indeed call you what you want them too if the rest of the family calls you the same thing.