In the traditional signature form, the month is written as an elegant name. And the year should be marked with official support, and the month should be based on the lunar calendar. So, if you say September is the September of the lunar calendar, your signature should be:
Late Autumn by Geng Zi/Late Autumn by Qiu Ji/Ju Yue/X X Book by Xuan Yue.
If it is September in the solar calendar, it should be August in the lunar calendar, and the signature can be:
Mid-Autumn Festival/Zhengqiu/Mid-Autumn Festival/Gui Yue X Book