Cathy, so happy for you a new baby is always wonderful. When my DGD was born, she had 2 grandmothers and 2 great grandmothers. My SIL's mother was Grandma, his grandmother was Great Grandma. So my mother became GG for great grandma and I became Bubbie (yiddish for grandma). I am almost 20 years younger than my SIL's parents, so I was in my 40's when my DGD was born. I wanted to be called "The Young Fun Grandma", but my DD the killjoy wouldn't let that happen - lol. When my DGD started talking she changed some of the names, my mother when from being GG to being Grandma Woof (she had dogs that would bark when the phone would ring - and DGD loved to hear the dogs).
YaYa is Greek for grandma, just a thought.