Common misconception.

July and August were renamed. The original names were derived from five and six. The extra two months that threw everything off were January and February. When 5-10 were named January and February didn't even have names, it was just that cold period when there was no planting or harvesting. There were a bunch of other changes to the calendar over the centuries before we got where we are too.

Decent overview here: https://study.com/academy/lesson/the-ancient-roman-calendar-history-months-saints.html