As Liquid points out, there are many routes to skiing fame, or infamy. In race, its as straightforward (not simple, but straightforward) as putting down great times as you race in race associations and high school, then getting recruited by colleges... pretty much the same progression as any professional athlete.
Then there is the freestyle competition route to the bigs. That means entering open competitions, big and small, on your own dime, and grabbing podium spots at these competitions. That gets you noticed, and can get you a sponsor. Once you're sponsored, you can enter bigger time comps, and build as you go. If you do well enough, you go from wearing everybody's brands on your clothes and equipment, to people wearing your brand on theirs.
Then there is the instructor big leagues. That's comparable to working your way up to the big time in a company (because that's what it is). You do your job well, grow a clientele, and your clientele is your reputation. Your instructor reputation spreads largely through that and through PSIA. The most well-known instructors are typically those in senior leadership and examiner postions within PSIA. In that context, instructors get to know their colleagues from other mountains, and reputation spreads quickly in that way.
Then there is the grassroots method to ski fame. When you reach a certain point in skiing proficiency, you realize that there is only a fairly small group of people on any mountain that are at your ability level. When you realize you are part of a very small group amongst a large crowd, it creates a sense of community. The best skiers on any mountain know each other, or at least know of each other. People talk, stories spread, and a certain local fame can develop. That local fame can have a lot of implications. Since you're talking about a group of hardcore skiers, many of them are going to work in the industry in one capacity or another. Brand reps, instructors, patrollers, etc. Once you're known on your hill, you find yourself having connections. Those connections might spread your reputation beyond your local mountain. Venues like EpicSki, TGR, and other forums help spread that rep as well.