January -- Janus's month

February -- month of Februa
Intercalaris -- inter-calendar month
March -- Mars' month
April -- Aphrodite's month
May -- Maia's month
June -- Juno's month
July -- Julius Caesar's month
August -- Augustus Caesar's month
September -- the seventh month
October -- the eighth month
November -- the nineth month
December -- the tenth month

A History of the Months

The original Roman year had 10 named months Martius "March", Aprilis "April", Maius "May", Junius "June", Quintilis "July", Sextilis "August", September "September", October "October", November"November", December "December", and probably two unnamed months in the dead of winter when not much happened in agriculture. The year began with Martius "March". Numa Pompilius, the second king of Rome circa 700 BC, added the two months Januarius "January" and Februarius "February". He also moved the beginning of the year from Marius to Januarius and changed the number of days in several months to be odd, a lucky number. After Februarius there was occasionally an additional month of Intercalaris "intercalendar". This is the origin of the leap-year day being in February. In 46 BC, Julius Caesar reformed the Roman calendar (hence the Julian calendar) changing the number of days in many months and removing Intercalaris.

January -- Janus's month

Middle English Januarie
Latin Januarius "of Janus"
Latin Janu(s) "Janus" + -arius "ary (pertaining to)"
Latin Januarius mensis "month of Janus"

Janus is the Roman god of gates and doorways, depicted with two faces looking in opposite directions. His festival month is January.

Januarius had 29 days, until Julius when it became 31 days long.

February -- month of Februa

Middle English Februarius
Latin Februarius "of Februa"
Latin Februa(s) "Februa" + -arius "ary (pertaining to)"
Latin Februarius mensis "month of Februa"
Latin dies februatus "day of purification"

Februarius had 28 days, until circa 450 BC when it had 23 or 24 days on some of every second year, until Julius when it had 29 days on every fourth year and 28 days otherwise.

Februa is the Roman festival of purification, held on February fifteenth. It is possibly of Sabine origin.

Intercalaris -- inter-calendar month

Latin Intercalaris "inter-calendar"
Latin Mercedonius (popular name) "?"

Intercalaris had 27 days until the month was abolished by Julius.

March -- Mars' month

Middle English March(e)
Anglo-French March(e)
Old English Martius
Latin Martius "of Mars"
Latin Marti(s) "Mars" + -us (adj. suffix)
Latin Martius mensis "month of Mars"

Martius has always had 31 days.

March was the original beginning of the year, and the time for the resumption of war.

Mars is the Roman god of war. He is identified with the Greek god Ares.

April -- Aphrodite's month

Old English April(is)
Latin Aprilis
Etruscan Apru
Greek Aphro, short for Aphrodite.

Aprilis had 30 days, until Numa when it had 29 days, until Julius when it became 30 days long.

Aphrodite is the Greek goddess of love and beauty. She is identified with the Roman goddess Venus.

May -- Maia's month

Old French Mai
Old English Maius
Latin Maius "of Maia"
Latin Maius mensis "month of Maia"

Maius has always had 31 days.

Maia (meaning "the great one") is the Italic goddess of spring, the daughter of Faunus, and wife of Vulcan.

June -- Juno's month

Middle English jun(e)
Old French juin
Old English junius
Latin Junius "of Juno"
Latin Junius mensis "month of Juno"

Junius had 30 days, until Numa when it had 29 days, until Julius when it became 30 days long.

Juno is the principle goddess of the Roman Pantheon. She is the goddess of marriage and the well-being of women. She is the wife and sister of Jupiter. She is identified with the Greek goddess Hera.

July -- Julius Caesar's month

Middle English Julie
Latin Julius "Julius"
Latin Julius mensis "month of Julius"
Latin quintilis mensis "fifth month"

Quintilis (and later Julius) has always had 31 days.

Julius Caesar reformed the Roman calendar (hence the Julian calendar) in 46 BC. In the process, he renamed this month after himself.

August -- Augustus Caesar's month

Latin Augustus "Augustus"
Latin Augustus mensis "month of Augustus"
Latin sextilis mensis "sixth month"

Sextilis had 30 days, until Numa when it had 29 days, until Julius when it became 31 days long.

Augustus Caesar clarified and completed the calendar reform of Julius Caesar. In the process, he also renamed this month after himself.

September -- the seventh month

Middle English septembre
Latin September
Latin septem "seven" + -ber (adj. suffix)
Latin september mensis "seventh month"

September had 30 days, until Numa when it had 29 days, until Julius when it became 30 days long.

October -- the eighth month

Middle English octobre
Latin October
Latin octo "eight" + -ber (adj. suffix)
Latin october mensis "eighth month"

October has always had 31 days.

November -- the nineth month

Middle English Novembre
Latin November
Latin Novembris mensis "nineth month"

Novembris had 30 days, until Numa when it had 29 days, until Julius when it became 30 days long.

December -- the tenth month

Middle English decembre
Old French decembre
Latin december "tenth month"
Latin decem "ten" + -ber (adj. suffix)

December had 30 days, until Numa when it had 29 days, until Julius when it became 31 days long.