Why do you think the protagonist in "To Build a Fire" is referred to as "the man" as opposed to being given a name?
A fiction writer typically gives characters names in order to enable the reader to tell them apart. Since there is no other human character in "To Build a Fire," Jack London had no need to give his protagonist a name. London must have had additional reasons for not providing him with a name. One reason could have been that he wanted to illustrate the insignificance of human beings in contrast to the grandeur and power of nature. The protagonist seems pathetically tiny and helpless in the vast frozen landscape, and his motivation seems pathetically simple. He just wants to stay alive, and he needs a fire to do so.
Other famous writers have created stories in which they did not assign names to their characters. Two that come to mind are Stephen Crane and Ernest Hemingway. In Crane's great story "The Open Boat" three characters are only referred to as the Captain, the Cook, and the Correspondent. According to the eNotes Study Guide for that story:
The oiler, Billie, is the only character in the story whose name is given. This fact has often been remarked upon by critics. He is also the only character in the open boat who does not survive the ordeal. He is the most physically able of the four characters and seems the most determined to survive. The strongest rower, the oiler also makes the strongest effort to swim ashore when the boat capsizes in the surf. Yet his efforts come to nothing—he drowns in the shallow water just off shore while the other characters are saved by what appears to be random chance.
In Ernest Hemingway's frequently anthologized story "Hills Like White Elephants," none of the three characters are given names.They are referred to as "the American," "the girl," and "the woman." Since the reader does not know these characters by name, it is almost as if the reader has not been introduced to them and has not been invited to participate in their story. The reader is deliberately kept at a distance and can only speculate about what is going on between the man and the girl based on what they say and do. Hemingway was noted for his so-called "iceberg theory." He tried to leave out everything that was not absolutely essential to the event he was dramatizing.
There is something very "modern" about this technique. We live in a world in which we see and hear many things that arouse our curiosity and even our sympathy but which we will never understand. Older writers felt a need, not only to introduce their characters, but to describe their backgrounds and personalities. Good examples are Chekhov's "The Lady with the Pet Dog" and "The Bet," as well as Tolstoy's "How Much Land Does a Man Need."
In some of the motion pictures by directors like Ingmar Bergman and Jean-Luc Godard, it is possible for the viewer to feel disoriented because the usual questions of who, what, where, why, and when are not answered. A good example is Ingmar Bergman's marvelous Through a Glass Darkly. The viewer is forced to use deduction and guesswork--but that is the modern condition. There are too many people in the world. Too much is happening all around us, and everything seems to be happening faster and faster.
To be truthful, we ourselves meet a lot of people and forget their names as soon as we have shaken their hands--if we ever caught their names in the first place. In Jack London's "To Build a Fire," if he had given his protagonist a name, such as Jack Carter, would we even remember it? And what difference would it make?