In Jainism there isn’t a tradition of naming months as September or December. Those are names from the Gregorian calendar used in the modern world.

Jain calendars typically name months according to the lunar/solar Jain system, using traditional names such as Chaitra, Vaishakha, Jyeshtha, Ashadha, Shravan, Bhadrapad, Ashwin, Kartik, Margashirsha, Pausha, Magha, Phalguna, and so on (and their corresponding lunar fortnights and tithis). The Digambar and Shwetambar sects may have slight differences in calendar calculations or festival dates, but both use the same traditional Jain month framework; they do not use separate “September” or “December” names.

If you’d like, I can explain how the Jain lunisolar calendar maps to the Gregorian months in a general way, or point you to a JainKnowledge.com page that discusses the Jain calendar.