It's Gracie Jiu-Jitsu if you learn it from the Gracies, or at least from those of the Gracies who are "authorized" to teach it. (I think I heard that some of them had sort of fallen out of favor, but I could very well be wrong.) In any event, I think they've got the term copyrighted.
So... if you learn it from someone else, it's "Brazilian Jiu Jitsu".
And, like any other martial art, folks take it and change it a little. Some BJJ is still gi-oriented, some has been modified for no-gi.