The names of the months are of Babylonian/Chaldean origin. According to the Ramban we use these names to remember our salvation from גלות בבל. Seven of the twelve names we use today are mentioned in the later books of Tanach. The earliest source that lists all twelve names is the תרגום שני on מגילת אסתר.
If the month names aren’t Hebrew, why do chazal make drashot/רמזים on the names?
What are the halachic ramifications of the names not being of Jewish origin?
Shiur provided courtesy of Torah Anytime