What is the meaning of the phrase "he was reminded that she was nameless" in the context in which it appears?

Close to the beginning of Kate Chopin's story "Desiree's Baby," there is a flashback that explains Desiree's background and how Armand fell in love with her. Desiree was a foundling; the Valmondes had adopted her after finding her along the roadside, "purposely left by a party of Texans." Desiree grew up as a neighbor to Armand, but he never took much notice of her until he saw her at the age of 18 standing against...

Close to the beginning of Kate Chopin's story "Desiree's Baby," there is a flashback that explains Desiree's background and how Armand fell in love with her. Desiree was a foundling; the Valmondes had adopted her after finding her along the roadside, "purposely left by a party of Texans." Desiree grew up as a neighbor to Armand, but he never took much notice of her until he saw her at the age of 18 standing against a pillar at her home. At that point he fell madly in love with her and decided he wanted to marry her. Although not specifically stated, it appears that Desiree's father, Monsieur Valmonde, was the one who reminded Armand that "she was nameless." Presumably when Armand approached Desiree's father to ask for her hand in marriage, Desiree's father gave him a warning. He made sure Armand knew that Desiree had been adopted and therefore no one knew about her ancestry.

Why should this matter? In the South at the time, laws and societal practices took one's race into account. If a person had black heritage, he or she would be subjected to discriminatory laws, and the white culture in which both the Valmondes and the Aubignys circulated would look down upon and reject anyone who was of mixed blood. Valmonde may have realized that Armand was particularly wrapped up in that culture. He had one of the wealthiest plantations in the area, and he was ruthless toward his slaves. Valmonde wanted to warn him that, should he and Desiree have children, any possible African heritage might show up in their offspring. Armand ignores this warning because of his passion for Desiree.

Later, of course, Desiree's baby does turn out to have African features, and Armand rejects Desiree and the baby because of that. The sentence "He was reminded that she was nameless" foreshadows what occurs later in the story when Armand tells Desiree, "It means that the child is not white....It means that you are not white."