There’s no recorded evidence of this though
King Numa added January and February to the beginning of the calendar year because the previous system with 10 months didn’t align well with the seasons. This pushed the rest of the months back by 2 giving us this weird remnant. Originally, months 5 and 6 also had Latin names based on the number of the month (Quintilis and Sextilis) but those were late renamed to honor Julius Caesar and his adopted nephew Augustus Caesar, which is how we got the names for July and August.
Edit: Added a comma
It’s actually Christians who moved the first month of a year from March to January, to celebrate the circumcision of Jesus, which is on 1-st January.