Why is the character "La Blanche" named as such in "Désirée's Baby"?

Your question refers to a character who is mentioned three times in Kate Chopin's story "Desiree's Baby". La Blanche is one of the slaves at the L'Abri estate where Desiree lives with her husband and infant. The first time La Blanche's name is mentioned is when Desiree described how loud her baby can cry; it can be heard "as far away as La Blanche's cabin". The fact that La Blanche has a cabin is a clue to us that she is probably one of the slaves.

The second time her name is mentioned is when Desiree's baby is three months old and "one of La Blanche's little quadroons" is doing the job of fanning the baby. La Blanche, then, is implied to be the mother of a child that is one-quarter black. If her child is one-quarter black, it must mean that his mother is half-black and his father is all black. La Blanche, as a half-black and ostensibly half-white person, may have been named "La Blanche" because her name means "the white" and because her skin was likely paler than the other slaves' skin color due to her heritage.

The third time La Blanche's name is mentioned is when Armand speaks cruelly to Desiree as she desperately tries to get him to agree that Desiree is white, even whiter than Armand himself. He replies that her hand is "as white as La Blanche's". Armand means that Desiree is only as "white" as a half-white person, and therefore is basically black in his estimation.

The irony of this, of course, is that we later learn that Armand himself is the one who had a black parent. We never learn anything about Desiree's true parentage. For Armand to use a comparison to La Blanche as an insult would be the height of hypocrisy if he had known that he too had one black parent. Unfortunately, Armand's belief that Desiree's bloodline is responsible for their baby's darkening complexion leads to Desiree's desperate decision to leave. We can only suppose that she and her baby have perished in the cold October forest, having left in clothing inadequate for the season. Armand does not discover the truth that his mother is black until after Desiree's disappearance.

The name "La Blanche" serves a primarily symbolic purpose. It means "white", and is thus directly connected to the issue of La Blanche's parentage. Furthermore, white is often used as a symbol for purity or innocence. When Armand compares Desiree to La Blanche in terms of color, it may be an attempt by Kate Chopin to say something about Desiree's (not to mention La Blanche's) position of being an innocent victim of racial prejudice. Desiree's clothing is white, she lies upon white muslin, and she is as white as a stone statue when waiting for Armand to read her mother's letter. The white imagery that runs throughout the story indicates that there is a question of virtue at stake in it.

"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.

Who is La Blanche in "Désirée's Baby"?

La Blanche is mentioned only in passing in this short story and only three times, but she is an important character, as she lends considerable context to the conflict of the story.

La Blanche's name is interesting: it means "the white one," even though she is clearly a Black slave who is the mother of a "quadroon boy." La Blanche's name implies that she is of mixed race and possibly that she has pale skin. If this is the case, she is considered to be Black only because she has Black heritage, not because of her skin color: something which is very important contextually.

When Désirée implores Armand to recognize that she is a white person with white skin, he says mockingly that her skin is indeed "as white as La Blanche's." The implication here is that it does not matter whether Désirée appears to be white: if she has an element of Black blood in her, then she and her child, like La Blanche, are deemed to be Black and seen as inferior.

It is also possible to argue that La Blanche is Armand's mistress. Désirée does not seem to notice anything odd about the fact that Armand has been visiting La Blanche's cabin, but to the reader, the detail is strange. There is a connection indicated, too, between La Blanche's child and Désirée's, which might be because both appear to be Black—or because both are the children of Armand.