Well, it's legit to use Noah so why shouldn't I give her the spelling I prefer? It makes me crazy how people always claim boys names get stolen by girls. NO-a (pr.) is strictly female. In Hebrew Noah (male would be pr. like Noach). So from its origin NO-a is feminine and the boys have stolen this one from the girls (at least the pronunciation).
With a feminine middle name that would be listed on all documents and class lists she wouldn't have any problems at all.