It seems like the names of the months are two places behind their number in the sequence... sorry if this isn't the right sub
EDIT: to make this clearer for people less familiar with Latin roots: septem means seven, octo means eight, novem means nine, and decem means ten.
The earliest Roman calendar had ten months, March-December. It was primarily an agricultural calendar, working on a lunar model. This calendar is not extant and must be reconstructed through speculation, but it's usually thought that there were no intercalary months between December and March, when there was little agricultural work. Instead those days appear to just have been unassigned days that were still counted but ignored for ritual purposes. Traditionally Numa brought the number of Roman months up to twelve and aligned it with the solar year, by adding January and February--there's some controversy in our texts as to whether Numa inserted February as the second month or the twelfth month, in which case the current order is due to the work of the decemvirs. It doesn't really matter much, though, because the traditional dating of Numa's calendar reform to the late 8th Century is clearly far too early, and the reform almost certainly dates from sometime during the early Republic. The OCD remarks that some authors believed that the Republican calendar was brought from the Etruscans by Tarquinius Priscus, which I personally am much more inclined to believe. In any case that's how the Republican calendar worked. Intercalary months were added every other year, at least in theory--in reality they could be added whenever the pontifex maximus wanted to, and they were kept very irregularly, which is why Caesar set the much more regular Julian Calendar in place. So the insertion of two extra months at the front of the calendar moved all the months back two, hence the two-month difference between the name of the ninth month and its actual calendar position
hi! fyi, you'll find lots on this specific question and more on the evolution of the calendar in the FAQ