You can thank the Romans for that. In the Roman calender, September was the 7th month, October was the 8th, November was the 9th, and December was the 10th. Now, let's see if you remember your Latin prefixes:
7 = sept
8 = oct
9 = non
10 = decCool, huh? I never realized that before. These are the valuable things I learn from naming organic compounds in chemistry.
We have twelve months now because "January" and "February" were added to the Julian calendar. The first month of the Roman calendar was March (named after Mars, god of war.) I propose that we use the following names to refer to the months:
June: Quadrober or Quartcember. Maybe Quadricember? No, Quadrober sounds best
then September, October, November, December
and February: Duodecember
Now we just need to think of better names for the days of the weeks...