I was going to point out both BatRonin's point about sub-jutsus, and also that in the old days, JuJitsu, Ju-jutsu, Yawara, whatever you want to call it was basically like Kung Fu in China, where everything was just a style of Jiu-Jitsu. The styles were denoted by school name (i.e.- Fusen Ryu... I've even seen translated texts with Judo being reffered to as Kodokan Ryu, which is pretty cool sounding).
That said, using the naming system set up back then with the Naginata Jitsu, Katana Jitsu, and so on... Wouldn't Brazillian Jiu-Jitsu be the art of gently fighting with Brazilians as your weapons?
You could walk around with a tiny Gracie in a pouch on your back, and if you came to a bridge with another guy that refused to let you pass, you'd both whip out your miniature Ricksons and go to friggin' town!
It'd be like friggin' Pokemon. "I choose you, Mata Leao!!"