The first clue that there will be some significant play on the idea of Laurie/Charles’s identity is in the opening paragraph when the mother tells us how significant a moment of change it is to see
my sweet-voiced nursery school tot replaced by a long-trousered swaggering character...
In other words, the first day of kindergarten brings a transformation that “replaces” the Laurie she thinks she knows with a “character” she barely recognizes.
Although this change is immediately apparent, once Charles enters the story the mother seems to notice Laurie’s behavior at home less and less. It’s as if the fictional Charles becomes much more interesting and attention-grabbing than the actual boy at home and school, which is typical of Shirley Jackson’s moral world in which the children put the adults to shame and the adults get the comeuppance for their assumptions and obliviousness.
Another hint comes when the parents ask about the identity of the troublesome classmate and Jackson tells us “Laurie thought” before replying, “It was Charles.” Jackson doesn’t suggest that Laurie has to recall or remember the name of the boy, but rather that he invents it, either pulling it out of the blue or having already decided before. Either way, we see Laurie is an excellent and natural liar but gets his parents so hooked on his daily reports of Charles’s mischief that they become increasingly blind to their actual child’s behavior.
Jackson is implying that it’s often impossible for parents to see their own children in a negative light, even when the clues are plainly evident. The deeper we see Laurie’s parents pulled into the Charles drama, the more Jackson heightens the suspense towards the big reveal which will contain the story’s tone of dark humor and puts some egg on the silly parents’ faces.