Back in the day, the only fighters who got famous were the ones who did choreographed routines in movies. Bruce Lee and Chuck Norris were amazing fighters in their day, but you know them because of the (awesome) films they made in the '70s.
While the sport is becoming much more popular, there are still only a handful of MMA fighters who achieve national recognition, and even those who do aren't widely known by people who aren't fans of the sport. Most people know who Tom Brady and LeBron James are even if they don't follow football or basketball. But do they know who Frank Mir or Tito Ortiz is?
You can certainly become known and respected to those within the industry, but most of them have gotten their heads so banged up that they probably won't remember you in ten minutes anyway.
Is it possible to achieve fame simply being one of the best MMA fighters in the world? Absolutely. Thanks to mainstream sports networks taking the UFC seriously as a newsworthy competition, the top fighters are becoming household names.
Chuck Liddell and Randy Couture are so famous that they're now in major Hollywood films. And if you've never heard of Ronda Rousey, you probably don't have access to the internet.
In which case, how are you reading this?