It was Mike (our chief editor) based on the page's history. Doing some research myself, it is indeed from Anahita, but via Ancient Greek Ἀναῗτις (Anaitis). For a full breakdown of Anahita's descendants with references, you can see here:
https://en.wiktionary.org/wiki/𐎠𐎴𐏃𐎡𐎫#Old_Persian . Also keep in mind that Old Greek and Persian existed over a thousand years before Old French.
As for Nina, while I personally think the coincidence is not particularly relevant, its orthographic and phonetic similarity may be of interest to some.