Two kinds of words that show the moon name are in Japan.

The one is "Old Style (or O.S.)" and  the other is "New Style (or N.S.)."
"Old Style (or the old [lunar] calendar)" is called "新暦[shin-reki] or 太陽暦[taiyou-reki]" in Japan.

"New Style (or the solar [Gregorian] calendar)" is called "旧暦[kyuu-reki] or 陰暦[in-reki]" in Japan.

"新暦or 太陽暦(New Style)" is chiefly used in Japanese calendar.

In Japan, the solar calendar has been used until December 2, 1872.

After Meiji-Ishin, Japanese Government changed bureaucrats'"Reward once a year" into the salary system.

But, June existed twice in this fiscal year.
Japanese Government has the obligation to pay bureaucrats the salary of 13 times a year.
So, Japanese Government changed "Style of the calendar" suddenly.
It is because Japanese Government did not want to pay bureaucrats the salary of 13 times.

The old calendar is used in the fortune-telling and the traditional event etc. in present Japan.
In a word, the reason why Japanese calendar changed was "Salary payment refusal at the moment" of Japanese Government.
Such "Selfishness of Japanese Government" is still continued.

Then, I show you these kanji today.

Old calendar and lunar calendar in kanji.

English	Japan's solar calendar	Japan's old calendar
January
February
March
April
May
June
July
August
September
October
November
December

Some Considerations on the Origin of the Names of the Months by Lunar Calendar.

<January; 睦月[mutsuki]>:
Mutsuki is a chinese letter for "moon" which represent the shape of crescent.
There are two alternate expressions. The first one means "right month".
I don't know why it is "right", probably the right beginning of a year.
The second one means "month of enjoying".
In new year days members of family come together and enjoy.

<February; 如月[kisaragi]>:
There are three alternate expressions.
Pronunciations are all same.
I do not know the meaning of the first alternate but most used.
Directly translating it means "like as moon."
The second one means "wear dresses over and over."
In this cold season, this meaning is easy to understand but it is incorrect origin.
In luna calendar, 2 correspond to March (nearly) and it is getting warm.
The third one is the right one.
It means "plants grows again."
The bird is "uguisu" a kind of nightingale who sing "ho-hokekyoh"
The third one is the right one.
It means "plants grows again."
The bird is "uguisu" a kind of nightingale who sing "ho-hokekyoh."

うぐいす[Bush warbler] that is Bird of spring of Japan.

<March; 弥生[yayoi]>:
The second alternate is another expression using phonogram called "Hiragana" (see the page of Japanese Letters.) and favored because of its soft appearance.
The meaning is "grow more and more" corresponding to the grow of plants in spring.
The letters in alternative expression are in the style of brush pen writing.

<April; 卯月[uduki]>:
By luna calendar used in older days, 4 was early summer and the blossoms of deutzia called "u" was thought as the symbol of April.
"gatsu" and "zuki" are pronunciations for .
There are two more pronunciations, "getsu" and "tsuki".

<May; 皐月[satsuki]>:
Satsuki is the chinese letter for "five."
The pronunciation should be "go-gatsu" but "satsuki" was borrowed from other alternatives. Ordinary japanese can not write down the letter .
The meaning is something like vivid.
Japanese recall refreshy weather with clear sky and cool breeze from the sound of "satsuki."
The last one is probably a simplified shape of second one. The direct translation is "fast month."

<June; 水無月[minaduki]>:
Direct translation is "no water month".
June is the most rainy season in the year.
In my boyhood, I was taught as follows.
Now that water is this much on earth, there would be no water in the heaven.
It is the origin of the name and I believed it until today.
But it seems incorrect consulting with some materials.
By luna calendar, rainy season is over in 6 and water is scarce when rice plants need water.

<July; 文月[fumiduki]>:
Direct translation is "literature month" or "letter" month.
There are two explanations for it.
One is that on seventh of this month Star Festival is held and people write letters of wish to the god, therefore this month is "letter month". Another one: In this month by luna calendar, night is getting long after mid-summer and there is a lot of time to read literatures, so this month is "literature month".

<August; 葉月[hadiki]>:
The meaning is "leaves month."
There are two explanations.
One is: By luna calendar, this is the month whe leaves of trees begin coloring and falling. Another is: it means the leaves of katsura which grows on the moon in this month of Moon Viewing.
August is the hottest season and whole of this month is school vacation.
Most of companies have summer vacation of more than one week in this month.

<September; 長月[nagaduki]>:
The direct translation is "long moon" in September by luna calendar, the length of night time is felt long and moon is seen long time.
Chrysanthemum is one of the most favored flower in Japan and used for the crest of the Imperial Family.

<October; 神無月[kannaduki]>:
Direct translation is "no god month."
In October, all japanese gods (see Japanese Christmas) gather at izumo area to have big conference.
Therefore no god is in other areas in this month.

<November; 霜月[shimotsuki]>:
Direct translation is "frost month". In November, it is getting cold and frost begin to cover land in the morning.

<December; 師走[shiwasu]>:
Direct translation is "teacher run".
In order to understand it, you must know that in older days, people bought everything on credit and must pay it at the end of year and schools were operated individual teacher and he had to collect the tuition fee by himself for his payment.
Teachers were very busy in this month.
Of course, ordinary people were also busy.
But teachers are usually enjoy rather noble life and his busy appearance was funny.

By Hararie