Fame
Come on—you're in the best fighting unit of the most powerful military branch in history. But if you tell someone what you actually do, you'll have to kill them. Save it for when you get out. It may be agonizing to keep such a secret, but it would be more agonizing for the other guy when you have to drop him from behind and snap his neck just to keep him from blabbing.
However, wait until your service is done and then drop it that you're a former SEAL at a potential bar fight and watch everyone gaze intently into their drinks all at once.
SEALs have something better than fame…respect. You've earned it and you carry it all of your life.
Here are some real People who were SEAL People: Jesse Ventura, former pro wrestler and Governor of Minnesota (not at the same time) was a Navy SEAL. Chris Cassiday, SEAL, became a NASA astronaut. And Rudy Boesch took his skills of forty-five years in the military and applied them to Survivor: Borneo.