The Haftorah this past week mentions the second month using the name Ziv. The orignal names of the months are discussed here: First-Temple-Era names of the Hebrew months? When did the original names of the months change?
The names of the months came up with them from Bavel. Talmud Yerushalmi Rosh Hashana perek one, halacha two. This Yerushalmi is mentioned in Tosafos Rosh Hashana 7a, d.h. Midivrei.
Most of the names are mentioned in megilas Esther and Nechemia.
We can estimate then, at least to the latest possible date, based on Achashveirosh's reign. Wiki states Ahasuerus is usually identified as Xerxes I (486–465 BCE).