In the final analysis, I am not certain if any one person can identify the most important event in the work. The reader has to select what they determine to be the most important event in their own mind, and connect it to the overall meaning of the work to them. In think that you can get different ideas as to what others feel the most important event might be, but since they will have their own justification behind it, the effectiveness lessens. In the final analysis, you will have to determine what you think the most important moment or event is in the work because it will be on your shoulders to have to justify the choice. Some would argue that renaming himself could be the pinnacle moment because it sets him on his path to live a new life. Another could be the events that cause him to pursue his new life. Based on your own reading of the work, you will have select what you think is the most important event. I think it might be cool to select your moment and then start a discussion forum on enotes comparing your selected event or moment with others'.
Chris McCandless lived in Washington D.C. He was a smart young man who attended college and did well but he socially isolated himself from others. He graduates from high school and takes a trip to the Mojave Desert where he almost dies. This demonstrates his impulsive nature and his lack of judgement at times.
In the book "Into the Wild" it is hard to determine which is the most important event. I think it is important to note that his relationship with his parents became strained after Chris learns that his dad fathered anchild outside of his marriage. Chris develops anger at his parents which results in him breaking away to go off on an adventure on his own.
However, his entry into the Alaskan Wilderness without experience as a hunter or knowledge of the land as well as his underestimation of the power of the wilderness and his own inadequencies led to his death. One of the most important moments was when he refused help from the truck driver who was dropping him off to take the Stampede Trail. The truck driver recognized that Chris did not have adequate provisions and tried to get Chris to let him take him to town to get more equipment and food supply. Chris refused. He left his map of the wilderness in the truck. Had he been better prepared he would not have died.