I would guess that there was once a time when the year had 10 months, and September, October, November, and December were litterally just "7th month, 8th month, 9th month, 10th month." If this was so, what calendar was it under, how did the days divide out, how were more months added, and why didn't the names change?
(Side note: was July once called Sextember? June Pentember? Etc.?)
I thought we had something in the FAQ about this...it is certainly a frequently asked question! But u/verrevert answered a similar question last year: