Coelho's The Alchemist is the perfect bildungsroman; that is to say, it is a story of the main character's growth, education, and personal edification from novice to expert. Some may also say it is a novel about rites of passage--those rituals one goes through in order to become an adult. "The boy," as Coelho calls him, is just that, until he completes his personal journey to find his treasure and learns the skills he needs to fulfill his personal legend. It is a story of growing from boy to man.
The narrator, however, seems to be one who perceives Santiago not unlike how a teacher or parent might speak about a son. For example, even after Santiago finds his treasure and fulfills his personal legend, the author/speaker still calls him "the boy" because he is still young and has his whole life ahead of him. Yet there still seems to be a certain parental/son relationship between the speaker and the boy, so "the boy" isn't dropped after all of the goals are achieved. Maybe another reason that "the boy" isn't dropped eventually is to remind the reader that even though he achieved his goals in many ways, he still wasn't completely a man until he returned to Fatima and started his next quest.