Fame is not completely unheard of for wrestlers, but it's unlikely for a collegiate wrestling career. Wrestlers who want to get famous tend to feed into one of three destinations.

The most obvious and on-topic destination is the Olympics. The nice part about becoming an Olympic athlete is that you can easily transition from there to professional wrestling or Mixed Martial Arts. The not-so-nice part is that it's kind of difficult to be an Olympic athlete. No, seriously. Ask anyone. And the Olympics usually offer only the most fleeting bit of fame for most wrestlers.

But at least you learn a proper heimlich technique. (Source)

The second option is so-called "professional wrestling." You'll be entering an athletic environment that, because it's an exhibition, is not governed like a sport. What does that mean? Well, no off-season, so tons and tons of nagging injuries. If you ever want a depressing hour of your life, Google "dead pro wrestlers" and be prepared for a long, dark night of the soul.

Your third potential gateway to fame is Mixed Martial Arts. This sport is just coming into its own, and a lot of wrestlers have found success here. Like any combat sport, there are serious risks, from the standard joint problems all the way up to the kind of brain damage you get when a giant man tries to open up your head like a coconut.