John Smith's name
John Smith is a famous man from the Colonial era. So, the white family who adopted this Native American orphan did him a disservice by encouraging him to find his identity in their side of the cultural divide, as if to prove something. This sets him on a path to be mistreated, because he obeys his upbringing to "live up to his name" but people mistreat him anyway because of the color of his skin. It is a symbolic reminder that they can't take his heritage away just by changing his name.
The racism motif
Undeniably, the novel points to racism as a problem. Although John starts murdering white people, he is only trying to live up to the cultural narrative that he was handed down through racism. In a way, his own racial hatred is an archetypal reversal of all the hatred that he received throughout his whole life, just for looking differently. That makes this a kind of horror story akin to German folklore where the risks of racism are blown way out of proportion for analysis' sake.
The hallucinations
The hallucinations are symbols for madness. They indicate the origin of his madness which is his desperate desire to be accepted (by anyone!) and his consistent battle against himself to believe in himself and support himself when his external reality has given him no suggestion to do that. He battles with shame until the point that the voices of shame become manifested through hallucination.
The symbol killer
As a serial killer, John Smith intentionally embodies a myth about his culture that was hateful to begin with. He is "living up to his reputation" for vengeance's sake by punishing white people for giving him such a hateful narrative about his own life. At least that is the symbolic effect of his character. Perhaps one can argue that he doesn't really see it this way and is legitimately crazy, but the murdering is sociopathic regardless.
The dilemma
Although the narrative depicted in this analysis is the suggested interpretation, there is a dilemma about the identity of the killer toward the ending of the book. Perhaps John himself is not the real killer. That means that other people might be using the dilemma presented through John's story to frame him for these murders—perhaps even Jack Wilson who shares the Native roots. This symbolizes the ubiquity of the problems symbolized by the killer. In other words, these problems extend past the specifics of this story.
Spiritualism as a symbol
When the novel ends with a Native American spirit dance, the suggestion is made that perhaps the boy was the murderer after all, but was possessed by the literal ghosts and spirits of his ancestors or other spiritual ancestors. This is a difficult symbol to address, because on its face, it is an offensive stereotype about Native American folklore and it is an offensive stereotype about schizophrenia, but as a symbol, it does point to the complexity of motivation. A generous reader might be reminded of the archetypes of the unconscious.