Steve,
Sorry for the confusion. I, too, get a bit confused when both names are so popular. The person is Anna Vecchia/Vechiaia Martorana.
Unfortunately, these type of American records typically do not include the parent's names. I would think, however, that if they did, they would mention her adopted parents.
The only other naturalization papers I could probably look into are the declaration of intention papers, which are the first step towards gaining citizenship. I'll have to do more research on that to see if she ever filled any out.
I'll keep you updated with that should anything come up. Thanks!