The protagonist in The Accident is left nameless for most of the novel. What do you think was the author's intent in doing so?

It's possible that Elie Wiesel left the protagonist nameless because he's living in the past and ready to die for most of the novel. Reclaiming his name at the end of the novel is symbolic of his desire to continue living and move into the future instead of being stuck in the past.
Other characters in The Accident have names; however, the protagonist and point-of-view character in the novel doesn't. He also isn't completely sure that he wants to continue living his life. He can't move on from the past, because it was so horrible and filled with trauma. It took away the people that he loved. It left him with an inability to share himself and his experiences with others.
He finally names himself when he explains a traumatic part of his past to Katherine, his girlfriend. In this way, he shows the reader a bit of hope that he might be able to move on from his traumatic past instead of keeping it locked inside him. He tells the story of how a teacher told him that when he died, an angel would ask for his name three times. He would have to answer not only that his name was Eliezar, but also that he was the son of Sarah. He worried he would forget his mother's name and be doomed to stay buried rather than go to Heaven.
This shows that he wants to move forward. He's able to be Eliezar to the reader and to the people in his life because he's decided that he can try to reclaim some kind of life despite what happened in the Holocaust. By naming himself in a moment of disclosure and connection with another person, Eliezar is choosing to be a different man. Instead of the person who is still held captive by the past, he's going to be someone who moves forward and accepts new connections with the people in his life.
It's important to note that saying his name is an important point for him but not the end of his healing. There isn't necessarily an end to the healing. It's an ongoing process that continues as he tries to overcome his trauma.