The name for a gym or dojo (i.e. a physical place) should end in specific words that evoke a physical edifice (堂 or 庵 or 館, etc.).
The name for a style, or school (of thought), like expressionism or cubism, should end in words that point in that direction (like 流 or 派 or 術, etc.). Jutsu, like ninjutsu or jujutsu (jujitsu), is the suffix for a lot of martial arts.
I'm not familiar with Raiju, but I guess it's this 雷獣? (Lightning beast) - so you might use 雷獣術 (Raijū-jutsu) if you are heading in that direction. That would mean "Art/Technique of the Raijū". A thought I had was that you could borrow from the "crouching tiger" theme, and use "crouching beast" 臥獣術 (Gajū-jutsu).