In French, the name, Desiree, means desired one, and Desiree is, in many ways, the desired one of the story. When she is found, as a baby, by Monsieur Valmonde at the entrance to his home, she is claimed by Madame Valmonde as her own. She believes "Desiree had been sent to her by a beneficent Providence to bet the child of her affection, seeing that she was without a child of the flesh." It seems that she was even named Desiree because a child had been so desired by the Valmondes. The little girl grew up to be kind, lovely, and beautiful, and everyone adored her.
Armand Aubigny seemed to fall in love with her in the same way; it was as if he'd been "struck by a pistol shot." In fact, he seemed to love Desiree so much that he didn't care if her background was unknown. Perhaps, even, her unknown background made her even more desirable to him: not only is she beautiful and lovely, but with an obscure origin, any child of theirs who didn't look like white could be attributed to Desiree's background and not Armand's. Thus, not only was Desiree desired for her beauty and personality but also for her unknown history which could be used to shield Armand's own origins, if necessary.
La Blanche is one of the slaves on Armand's plantation. Because she is so fair-skinned, she is most likely the product of rape between a black (or part-black) female slave and a white master, and her name means the white one, referring to her skin tone. It seems possible that Armand is actually raping her. Desiree tells her mother that "'Armand heard [the baby crying] the other day as far away as La Blanche's cabin.'" But what reason would he have to be in a slave woman's cabin? I can think of only one. Often, fair-skinned slaves were thought to be more desirable than darker-skinned ones to white masters, and it was not an uncommon practice for masters to rape their slaves.
If this is true, and it's not possible to know for sure, then this casts more doubt on Armand's character. He's already a slave-owner, which makes him morally repugnant. If he is having sex with a slave, then he is a rapist. If he's having sex with anyone, then he is cheating on his wife, a wife that he seemed to desire so greatly. Can we put it past such a man to marry a woman whose unknown heritage could protect his own? I don't think so.
Further, the name of his plantation, L'Abri, means the shelter, and it certainly is a shelter for Armand, if not Desiree. His family property and name, one of "the oldest and proudest in Louisiana," protects him from suspicion about his race despite his "dark . . . face." No one questions Armand's heritage as a result of his shelter, his family's plantation and name, and so its name seems quite appropriate.