I listened to the audiobook version some time ago, the details of which I am a little hazy on, so I can only speak to the character in the movie.
In the movie Christopher McCandless graduates from college, remarking to his dad that he believes his grades are good enough to get into Harvard Law. He then donates his savings to charity and sets off on a road trip in his old, beat up car. Shortly after abandoning his car, he burns what money he has left and begins hitchhiking, where he comes across various interesting characters. Somewhere along the road he decides to give himself a new name and settles on Alex. I am not sure whether this name is meant to make it difficult for his family to track him down, whom he seems to have problems with, or whether he was shedding his old identity and adopting a new one.
Whilst I am by no means an expert on Dudeism, Alex seems to be, according to my understanding, very dude-like. He very much lives in the moment, he is non-violent, doesn't take advantage of people even when the opportunity presents itself, and doesn't consider himself to be above other people despite his obvious intelligence.