Ugh I hate cheaters. Once a cheater - always a cheater. This man might just think it is all in fun, and might not even realize the nickname he has been given. Maybe consider speaking to him about it before the round, a day or so before, privately of course. Simply say that although you are sure his morals are intact, there have been rumors going around that he cheats. And that you do not want these rumors to persist.
If you do not feel comfortable doing this, walk up to him on the first tee, shake his hand, look him in the eye, and say "I am looking forward to a fair round today - hopefully you are as well"
If you see him doing something - immeadiately call him out. Don't be embarassed to follow him around - chances are you will spook him so bad he will be scared to do it! :)