Author Jackson used several phrases and clues in the story to let the reader infer that Charles is really Laurie, or rather a figment of Laurie's imagination. On the first page of the story, when questioned by his parents about Charles' misbehavior the author writes that Laurie answered "...addressing his bread and butter..." rather than by answering his parents directly while looking at them. Laurie then walks off rather than answer his parents.
Later in the story, Laurie arrives home late full of stories about Charles' antics and states that Charles had to stay late after school for his misbehavior. Ironically, his parents do not seem to realize what the reader immediately sees in that connection.
Lastly at the end of the story, Laurie's mother meets his teacher and mentions Charles' disruptions. His teacher replies that there is not a "Charles" in class. Obviously, Charles acts out as he does due to Laurie's actions since they are one in the same. Laurie has a strong character and is independent enough to want to experiment, as a kindergartner, with who he really is. He is experimenting with different personalities, perhaps to get his parents' attention, perhaps even to get into enough trouble to have to stay home.