Also July and August already existed, but they were renamed:
"July is the seventh month of the year (between June and August) in the Julian and Gregorian Calendars and the fourth of seven months to have a length of 31 days. It was named by the Roman Senate in honour of Roman general Julius Caesar, it being the month of his birth. Prior to that, it was called Quintilis, being the fifth month of the 10-month calendar."
"August is the eighth month of the year in the Julian and Gregorian calendars, and the fifth of seven months to have a length of 31 days.[1] It was originally named Sextilis in Latin because it was the sixth month in the original ten-month Roman calendar under Romulus in 753 BC, with March being the first month of the year."