In the pre-Babylonian era, we find in the Scriptures only four months on the calendar that are identified by name:
The first month (Nissan): Aviv
The second month (Iyar): Ziv
The seventh month (Tishrei): Eitanim
The eighth month (Cheshvan): Bul
The other months were just known by their place in the calendar—e.g., third month, fourth month—starting from the first month: first by virtue of the fact that it is the month when our nation left Egypt, the month when we became a nation.
(Apparently, even the four months that had names were more often than not referred to by their numeric place on the calendar, with the names serving as secondary titles accompanying their numbers.)
The Jerusalem Talmud tells us that the modern names of the months “came up [to Israel] with [the returnees] from Babylon,” at the onset of the second Jewish commonwealth, approximately 350 BCE.
So, why did we begin to use these names? Why didn’t we stick with the biblical practice of referring to months by their number?
Nachmanides suggests that this is consistent with Jeremiah’s prophecy: “Therefore, behold days are coming, says G‑d, and it shall no longer be said [by one who wishes to pronounce an oath], ‘As G‑d lives, who brought up the children of Israel from the land of Egypt,’ but rather, ‘As G‑d lives, who brought up the children of Israel from the north land [Babylon] . . .’”
The original system was to count months in numeric order, starting from Nissan. Thus, any time a person mentioned a month, he was in effect recalling the exodus from Egypt: we are in, say, the sixth month—six months since the month of the Exodus. Thus, the numeric naming served as a constant reminder of our deliverance from Egypt.
After we were delivered from Babylonian captivity, however, we started using the names that we became used to using in Babylon. And now, these names served to remind us that G‑d has redeemed us from this second exile.
I hope that I’ve been helpful today.
Rabbi Menachem Posner