Exorcists don't usually get famous, but there are a few exorcists of note. Perhaps you've heard of Father Gabriele Amorth? He's apparently performed tens of thousands of exorcisms, and is one of the founders of the International Association of Exorcists (IAE). And if not him, how about Father Jeremy Davies, the co-founder of IAE, who famously believes that acupuncture, yoga, and even Harry Potter are "caused" by a "contagious demonic factor"?
And who could forget Father Damien Karras? He may be a fictional priest (you know, the one from The Exorcist), but he's definitely the face of exorcists in many people's minds.
No, you probably won't get famous, but don't feel too bad about it; fame is probably a terrible idea for an exorcist anyway. Think about it: if you're famous, the devil already knows who you are before you even show up to attempt to destroy him. Obviously, he's going to take the time to research how you work ahead of time, and that isn't the sort of disadvantage you want to be walking into, no siree.