I separate into 2 parts : Part 1 - Name of archaic months and their meaniings and Part 2 - The meaning of SS characters relate to archaic months.
Thank to C.K Gan who allow me to link to his page!
1.Mutsuki
-
The archaic name for January. Also read
as "Mutsubizuki". Etymological word was unknown but in poetry, it
always means the month of affection when members of family, relatives and
friends join to celebrate the New Year.
2.Kisaragi
-
The archaic name for February. Etymological
word was said to be 
(Kisaragi) means the rebirth of plants and trees, or 
(Kinusaragi or Kisaragi) means putting more clothes against
the cold weather. (In Japan, February is said to be the coldest month of
the year)
3.Yayoi
-
The archaic name for March. Etymological
word was said that it was transformed from 
(ya-oi) means the thickly growth. The word 
(ya or iya) is a prefix, sometime it means "many".
4.Uzuki
-
The archaic name for April. It means the month
in which 
(U no Hana) or the flower of Deutzia blooms.
5.Satsuki
-
The archaic name for May. The word "Sa",
is omitted from 
(Sanaezuki), means the month of planting rice shoots.
Sometime it also can be written as 
(Satsuki). The word 
is a prefix, no meaning. For another example : 
(Sa-otome)
The archaic name for June. Also read as
"Minatsuki".
Although literally, it means the "waterless month", etymological word has
various views. Some said that "Mi" refers to water and "Na" is a word added
for euphony. So, the original meaning may be "Mi no tsuki" or "Month of
water". (June is the month which has the most rain of the year).
7.Fumizuki
-
The archaic name for July. Also read as "Fuzuki"
or archaic, "Funzuki". Literally, "month of letter". It has various views
on etymology. Some peoplementioned that the original was from the late Heian
period (794-1192) which said that July was the month for writing a letter with
casual language. Some people that because of Tanabata Festival (on July 7),
people wrote a poem in Chinese characters. So it can be said that it was the
month of poetry.
8.Hazuki
-
The archaic name for August. Also read
as "Hatsuki". Etymological word was unknown, but It refers to
the month of falling leaves. In an ancient story, it said that around this
time, leaves on the moon changed into light yellow which made the moon
became more delight.
9.Nagatsuki
-
The archaic name for September. Also read
as "Nagazuki". Literally, "Long month", or sometime refers to "Long
moon". Because poets appreciated the beauty of full moon through out long
nights of the spring.
10.Kannazuki
-
The archaic name for October. Also read as "Kaminazuki"
or "Kamunazuki". Literally, "godless month". The legend said that large
numbers (Yao-yorozu)of gods from places in Japan, leave their homes
to assemble at Izumo Taisha or the Grand shrine of Izumo (now located in Shimane
Prefecture) to match soul mates for human. So, there were no gods remains in
local shrines. In Izumo, people called this month 
(Kami-arizuki) or "month of gods".
Large Number, in this case, is the word11.Shimotsuki -(Yao-yorozu). Although literally means 8 million, in Archaic Japanese, the word "Ya" means "many". So, the word Yao-yorozu should means "great numbers".
The archaic name for November. Literally, "month
of frost", because in Japan, winter begins at early November. Dew becomes frozen
from the northeast of Japan. It was named to reminds farmers to get ready
for winter.
12.Shiwasu
-
The archaic name for December. Also called 
(Gokugetsu) or (Gokutsuki). The word "Shi" refers to a priest, literally,
"running priests". It always means to "month of busy priests". In the past,
it was a custom that priests must went to houses to attend religious services
to Buddhists. Around the end of a year, priests would be busy going to places
and it also showed how people be busy at the end of a year.
1. Hazuki 
It is the name of the younger sister of Kazama brothers, "Kazama Hazuki". Don't expect that she was named "Hazuki" because of her birth month. In fact, her birthday is March 20, 1772. I think that her name was just named harmoniously with her brothers', for the word2. Minazuki(moon or month). And it is possible that the designer want Kazama brothers' appearance as primary colour (Sogetsu : blue <water>, Kazuki : red <fire>, Hazuki : green <leaf>).
It is the surname of Zankuro. It is homonymic and different from the archaic name of June in the first letter. The archaic name for June is3. Yayoi. (see meaning of the letters at the part 1)
The first letter of the surname
, is a character of Jikkan or the Ten Celestial stems. The full reading is "Mizu-no-E", means the big brother of water. (Please see more details about Jikkan here)
So,
This name does not directly concern to SS story. It is a name of an additional character in Sogetsu and Kazuki's short Drama of SS4 Arrange Soundtrax CD. If you want to read the story of the drama, please see CK Gan's SS4 Drama page.I guess that the name Yayoi, may be something like a duplicated Hazuki. From the story, we know that Yayoi looks very similar with Hazuki. So, I think is it possible that the writer of the story chose Hazuki's birthmonth to named for this character? (I just guess, because no any detail about this character)
