Dear Ashikaga & GreenCat,
I am glad that you both spent your precious time to try to help me out...
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We love the first option as it is the most appropriate one for our school.
We are grateful to you for trying to help
Thanks
Um, you are making a quite important decision...
I do not know if I can really help because there are numerous styles already and names should be unique, succinct and yet descriptive.
Anyway, there is one thing I must ask. Are you are making a new style?
I mean if your Dojo is a part of ready existing style, I do not think you are encouraged to give your Dojo any creative name.
As to Katate, which I do not really know much about but, its origin is very ambiguous in my opinion because Karate originally was spelled 唐手; It was during the war period or right before when the name was converted into 空手. The origin of Karate-do itself is predominantly Ryukyu Kingdom(Now called
Okinawa), of cause , and while there is no great deal of correlation with currently surviving Chinese Martial Arts, I expect people did import things.
My point is that Karate-Do can be said to be a Japanese thing and indeed a lot of things particularly some part of the philosophy associated was ripened by the martial artists who lived in Japan(Maybe not necessarily by of Japanese origin though). Nevertheless, Karate-do is a thing which was developed and tempered by the long line of martial artists who sought the strength, responsibility and virtue of an independent and free thinking person, which means Karate-do belongs to the martial artists who practice it rather than a country or culture.
I believe opinions vary, but well, if you are an martial artist who dedicated yourself for the art, both in physical and philosophical aspects, then unless you would like some Japanese tinge in the name, you do not necessarily have to include Japanese in the name of your style.
It is almost impudent and irreverent of me to be saying this, and some people would strongly oppose, but if there is anything like the spirit of Karate-Do, then it probably resides within the teachings and skills not in the names.
Having these rather silly things said, I will, at least, give it a shot translating the word "enlightenment".
Firstly the direct translation 啓示 啓発 教化 sound too religious and lofty because all of them are to do with leading the others and does not include the humble attitude of searching the path oneself.
So I check out something in the line of seeking-the-way. With key word "求道" I got the following results(use of the word "Light" for names of organisation in Japanese can imply something religious nowadays, probably better avoided):
http://thesaurus.weblio.jp/content/求道
求道
行 ・ 修身 ・ 修養 ・ 修行 ・ 精進
or 究明(きゅうめい)
（事件の）調査 ・ （容疑者の）追及 ・ （真実の）探求 ・ 追求 ・ （疑惑の）解明 ・ 謎解き ・ （真実を）追い求める ・ （問題を）明らかにする ・ （事実を）掘り下げる ・ （真犯人を）つきとめる
For words that could stand for peaceful, I check 茶道 terms:
茶道｜日本文化いろは事典
千利休の教え
現在の茶道の原型を完成させた千利休は茶道の心得を、「四規七則〔しきしちそく〕」と説きました。
「四規」とは和敬清寂〔わけいせいじゃく〕の精神を言います。
和…お互い仲良くする事。
敬…お互い敬いあう事。
清…見た目だけでなく心の清らかさの事。
寂…どんな時にも動じない心の事。
「七則」とは、他人に接するときの以下七つ心構えです。
「茶は服のよきように点て 炭は湯の沸くように置き 冬は暖かく夏は涼しく 花は野にあるように入れ
刻限は早めに 降らずとも雨具の用意 相客に心せよ」
つまり、「心をこめる、本質を見極め、季節感を大切にし、いのちを尊び、ゆとりをもち、やわらかい心を持ち、たがいに尊重しあう」のが大切だということです。
この他に千利休の教えをはじめての人にもわかりやすく、おぼえやすいように、和歌の形にしたものを、「利休道歌〔りきゅうどうか〕」といいます。
There are many possible combinations and the names carry important meanings, so you should really consult someone who knows what the important principles for your style. But well, at your request I tried to make up some a name.
敬心究明流
敬心求道流
敬 respect
心 heart of feelings
究明(To reveal, reason, seek, study)
求道(Seeking truth in religious or non-religious fashion dedicatedly)：
姦淫罪（かんいんざい）の意味 - goo国語辞書
It just came to me when I was trying to come up with the name, that the reason many of the Martial arts styles tend to use hard Chinese characters for their names is because that way they sound more masculine and strong...and the name I made up above does not really have the friendly hook.
I think it is generally considered more elegant and friendly to use a simple name that you can add figurative or metaphorical meaning. Also, it is probably better to avoid either vigorous or resolute words in names, because in frenzy people do all sorts of things. Something sounds serene, natural and yet beautiful: after all the reasons behind the name can be explained to visitors, right?
In the conclusion, I cannot really help you much at this as the decision is very important one, if you are setting up your own style, then it requires someone who is knowledgeable about the backgrounds of you style.
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For reference, I found the list of major Karate styles on the web.
1.極真会館
2.正道会館
3.大道塾
4.佐藤塾
5.拳道会
6.白蓮会館
7.誠道塾
8.芦原会館
9.逆真会館
10.士道館
11.禅道会
12.心道流心道会
13.寛水流
14.真武館
15.国際大山空手道連盟
16.誠武館
17.玄和会
18.清心流
19.極至塾
20.円心会館
21.錬志会館
22.賢友流
23.武心会館
24.剛心会
25.全日本新空手道連盟
26.松涛館
27.和道流
28.剛柔流
29.糸東流
30.新体育道
…私が知ってるだけでも30流派！空手に関しては流派によって技術体系､ﾙｰﾙ､思想が違う｡よって同じ空手でも流派が違えば別の格闘技だと位置づけるべきだ｡
茶道 流派
https://ja.wikipedia.org/wiki/Category:茶道流派
古武術
古武道HP（流派毎）