Why do you think "La Blanche" had that name?
"La" is a feminine article, and "to blanch" means to make white or pale by extracting color; to bleach. Example: Michael Jackson blanched his skin. So, "La Blanche" literally means "the white female." At first, we think it refers to the baby, but as we uncover Desiree's mother's secret, the white one refers ironically to Desiree herself. In other words, Desiree is not entirely white.
Desiree's baby is working in the opposite direction of Michael Jackson; it is attaining color instead of extracting it. The baby is born white, and then it begins to attain color as the pigmentation sets in. The baby begins to look brown, or mulatto over time, and rumors that Desiree fathered the child with a black man are spread around the plantation. The name is ironic because Desiree expects the baby to be white because she is white and the father is white, but her mother knows that Desiree is not entirely white.
White also has connotations according to the color code: "white is right"; "white is might"; white is blameless, pure. By contrast, black is symbolically corrupt, evil, etc... So by the end, the reader and Desiree realize the irony of the situation, that although Desiree is blameless for having relations with a slave (her mother is the guilty one), Desiree and her child will be blamed for it. The mother and child have violated the color code; the mother will never be blamed.
mstultz72: Your answer is completely wrong, you clearly misunderstood the story.
First of all, "La Blanche" is the name of a black slave woman who is owned by Armand. It is not a "nickname" for either the baby or Desirée. That is clear when Desirée says:
Armand heard him the other day as far away as La Blanche's cabin
Only slaves would be living in a cabin at the plantation.
Second of all, it is not Desirée's mother who is the carrier of the black blood, it is Armand's mother:
... it was part of an old letter from his mother to his father ... "But, above all," she wrote, "night and day, I thank the good God for having so arranged our lives that our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery."
So you see, Armand is actually the carrier of the "flaw", not Desirée, and this is the true irony of the story. So when he says to Desirée that her hand is as white as La Blanche's, he really says that even though she looks white, she's black. He's of course proven wrong at the end.
Finally, there is never any indication that Armand suspects Desirée for having relations with a slave. He simply believes that, because of her obscure background, she must be the one who has a black ancestor in her family line.
La Blance is the name of one of the slaves that Armand owned.