I highly doubt that any prebiblical text exists which mentions either of these ancient Hebrew names (Hannah, and Yohanan/John), and you are probably not going to be able to research this much further. At the least, however, Hannah and John are two entirely separate names, and the earlier recorded form is Hannah.
Your acquaintance's comment does not make much sense. Does s/he believe that every ancient female name necessarily derived from an even older male name? And it is certainly a verifiable fact that the name Ann vastly predates Ian.