Congratulations phizz! How wonderful to get to be a GGM and well and active enough to enjoy it! How wonderful, too, for the boy to have a living GGM though I realize he doesn't know or appreciate that yet, LOL!
But that's just the thing - it will be a long time before he even gets the meaning of that, won't it? So I wouldn't worry too much about the name. If "Gaga" suits you, however, and the parents are ok with it, then I think Gaga it should be.
Wishing you all many joys with this new baby and your growing family!