Sam
another example
The school year starts in September (lets say September 1) . Nonetheless on the first day of school the teacher writes on the Board 9/1. Throughout the first month pf school the months is labeled “9” the second month is “10”. The teacher doesn’t say well its the first month of school so lets call the date 1/1 then label October 2/ etc
Lehavdil the first month of the Jewish year is chodesh hashvii. We don’t change its name to “1”