Only a few names of the month were derived from Roman deities. Most simply came from the numbers of the months, or, as in two cases, in honor of Roman emperors.

January
Named after the Roman god of beginnings and endings Janus (the month Januarius)

February
The name comes either from the old-Italian god Februus or else from februa, signifying the festivals of purification celebrated in Rome during this month.

March
This is the first month of the Roman year. It is named after the Roman god of war, Mars.

April
Called Aprilis, from aperire, "to open". Possible because it is the month in which the buds begin to open.

May
The third month of the Roman calendar. The name probably comes from Maiesta, the Roman goddess of honor and reverence.

June
The fourth month was named in honor of Juno. However, the name might also come from iuniores (young men; juniors) as opposed to maiores (grown men; majors) for May, the two months being dedicated to young and old men.

July
It was the month in which Julius Ceasar was born, and named Julius in his honor in 44 BC, the year of his assasination. Also called Quintilis (fifth month).

August
Originally this month was called Sextilis (from sextus, "six"), but the name was later changed in honor of the first of the Roman emperors, Augustus (because several fortunate events of his life occured during this month).

September
The name comes from septem, "seven".

October
The name comes from octo, "eight"

November
The name comes from novem, "nine".

December
The name comes from decem, "ten".