Musser Zoger: The name Ester is also mentioned in the Megillah. That doesn’t make it Hebrew.
YehudahTvzi: Rav Schachter explains why we call the months by those names when according to the Ramban there is an Issur D’Oraisa in naming the months. He says we rename the months as a Zecher to major Geulos. Thus, the numbering go from Pesach and the names from Purim.