Thank you everyone for the suggestions and advice. Even the negative and highly opinionated ones! I think Cindy76 missed the whole point of my question.
I grew up in a wonderful little community on an island in Canada. People who we were close to but weren't family got the titles Aunt or Uncle. Then as they aged the whole community added the titles Aunt or Uncle to their names as a sign of respect, caring... inclusion.
Long before the slogan "It takes a whole village to raise a child" became popular, our communities (called outports here in Newfoundland) was living that belief. My husband's marriage broke up due in NO part to anything he ever did and he raised his boys alone with love and respect. He chose his second wife (Me) very carefully and his boys know that and respect me for what I have brought not only to his life but to theirs as well. For my granddaughter a beautiful 3 month old to call me by my first name would teach her that this adult is not to be respected, when she is calling other adults around her Mr. or Mrs. SO I did indeed need a special name. One that everyone including the woman who left her daddy when he was a little boy could feel comfortable with.
I chose Gigi. It stands on various days for Grumpy Granny, Gorgeous Granny, Glammy Granny, Good Grandmother... All I know is that Matthew uses that name all the time when he talks to Natalie ( MY granddaughter) and I like it. My own children were delighted that I am saving the special name of Nan or Grandma for their children and Natalie is blessed to have a loving and caring person in her life who will enhance her life and that of her extended family.
And my believe is that if we all cared a little more about the people who aren't related to us by DNA the world would be a safer and more peaceful place to be.