Hmm, at first thought, just the name 護身館, Goshinkan, has a nice sound to it (and basically means, "hall of self-defense), but I ran a search and that exact name is already being used: Goshinkan karate already exists as a school of Goju-ryu following Gogen Yamaguchi's lineage, under the Gojukai association:
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There's also a style of jujitsu called Goshinkan:
Goshinkan Ju-Jitsu
From what I've seen, there are a couple different formats that are common with Karate group names. Most names that use Japanese are a single jukugo (kanji compound), usually making a 3-part name. The longer names tend to be more descriptive, and far less catchy.
As I mentioned, Shotokan itself is an example of this: Shōtō was Funakoshi Gichin's penname: 松濤, meaning the wave-like motion of pine needles in the wind. This name may also be a nod to Matsumura Sokon, 松村宗棍, one of the grandfathers of Okinawan karate (松 shows up a lot in Okinawan karate styles). Funakoshi himself never named his style, only calling it "karate," but his students apparently made a sign for his dojo that read 松濤館: Shoto's Hall, and the name stuck.
Other styles combine words or characters:
剛柔流 (gōjū-ryū, hard-soft style),
極真 (kyokushin, ultimate truth),
一心流 (isshin-ryū, whole-heart style),
糸東流 (shitō-ryū, the characters coming from the names of 糸州 安恒 - Itosu Anko and 東恩納 寛量 - Higaonna Kanryo)
You're trying to name a group and not a style, but you can try to apply similar conventions if you want a name that's derived from these Japanese words. It's hard to use those two full words together unless you don't mind something long, like Goshin Chikaku Dojo...
If you're ok with a longer name and want the whole words to be used, you could go with something like: 知覚護身術 - Chikaku Goshinjutsu, which is kind of like "perception self-defense art/technique"
Goshinjutsu is already a word meaning "art of self defense," so adding Chikaku before that could help make the name unique. Using "jutsu" does sound a bit like its own style or martial art though. And there is a goshinjutsu karate style in the states, so you might need to add "Shotokan karate" or something, to delineate yourself:
Goshin-Jutsu - Self-Defense Karate
So like I said, it gets more descriptive, but longer and less catchy: 知覚護身術松濤館空手, Chikaku Goshinjutsu Shotokan Karate. You can also tack these on the end to specify
道 - way, as in karate-do
道場 - dojo, indicating a fixed location dedicated to the group's practice
会 - group, association
部 or 倶楽部 - club
Otherwise we're trying to combine the words to create something unique that rolls off the tongue...
So, if we were to mix goshin and chikaku together, what could we come up with? I'd like to be careful here because we're looking at creating words that don't exist, and I would run it past native Japanese speakers so there's no unintended meanings or readings...
The characters 身 (shin, mi) and 知 (chi) by themselves mean "body" and "knowledge," respectively. 護 (go) and 覚 (kaku, satori) being "protect" and "sense, learn, remember." I think these latter two characters carry the "meat" of the meaning, and could be useful for a compound name.
護覚 has no meaning, but looks a bit like it could mean "protection sense/awakeness," but I'm not a huge fan of "gokaku" as a name, especially when you add on the organizational indicator like "~kan" or "~kai." Japanese does weird things when you sandwich certain sounds together.
覚護 is also not a real word, but it reverses the order of "awaken, sense" and "protect." Another fun thing is if we read this as "kakugo," it becomes a homonym with 覚悟, a term that refers to the kind of preparedness a warrior brings to battle. Also, although it's a lot of plosives, it sandwiches a voiced plosive "g" in between all those unvoiced "k" sounds... 覚護会 "kakugo-kai", which has a better cadence in my opinion. You could also replace 会 with 空手道会 (karate-dō kai, karate-do group), 空手道協会 (karate-dō kyōkai, karate-do association). Just hearing that sounds a bit like "group/association that is ready for battle," but then when you see the name it has the protection meaning added to it.
Personally, I could also see a simple descriptive name for the group, and then using those two words on the logo/badge design to highlight their importance, but I understand you want to work them into the name itself. Perhaps we should call for help from
@Toritoribe before I get too creative with my new kanji compounds.
