I get the appeal of
Nan, but I know that I definitely wouldn't want to be called
Nan, and that makes me hesitant to put it on a child. I do think that the grandmother connotations make it a poor fit for a given name. I think that it could be cute as a nickname, and then if the wearer decided that they didn't like it they could drop it. Maybe
Anna called
Nan or
Hannah called
Nan?
I actually think that I like
Non slightly better than
Nan, but again I think it would have to be a nickname.
This might be a it of a stretch, but perhaps
Non could be a nickname for something like
Manon,
Rhiannon, or
Shannon?