I've finally started seeing McDojo BJJ. People don't actually call it BJJ. They say they are running a Mixed Martial Arts school that teaches Jiu-Jitsu, and Grappling. For example:
It's hard for someone in the general public to tell the difference.
You can teach TKD and judo and call it "mixed martial arts". MMA is a sport, not a style or a specific collection or combination of styles. This is one reason I have never liked the term MMA as a moniker for the sport. It's too generic.