This name is a figurative representation of what he is for other characters. He is used as a sacrificial lamb and a scapegoat for those such as McEachern and the dietitian as he grows up and is developed as a parallel to Christ. This is also an ironic name as his violent behavior is in opposition to Christ’s teachings.
His characterization is also symbolic. Just his belief (rather than knowledge) that he is of mixed race is enough to inspire racism in others and thus demonstrates how ludicrous racism is. Because he believes this to be true, he suffers from the agonies of self-loathing and the hatred of others. Racism is seen, therefore, to be both ludicrous yet life-defeating.
There are several examples of pointless secrecy given in the novel, such as Mrs McEachern hoarding money and Miss Burden hiding love letters. Secrets are seen to be kept for the sake of it and are a form of power for the powerless. This secrecy is aligned with femininity as these female characters are described as preferring subterfuge to emotional honesty.
Christmas is exasperated with this form of manipulation and despises his adoptive mother for trying to make him collude with her, yet he also behaves similarly with the women in his life. For him, secrecy represents deviousness and for this reason he even prefers the straightforward brutality of McEachern. This point helps to explain why his belief that he is of mixed race is the worst kept secret of the novel.
The reward for the capture of Christmas comes to represent greed and injustice as Brown seeks to profit from his friendship and the fact that Christmas has murdered Miss Burden. The narrative takes a moral turn when Brown is taken to Lena and their newly born baby under the pretence that he is going to the cabin for his long awaited reward.