In "Desiree's Baby," what is the meaning of the phrase, "He was reminded that she was nameless" in the context in which it appears?

In Kate Chopin's "Desiree's Baby," the child Desiree is found and her heritage is not known. Her adopted parents, however, don't care what her background is because they instantly love her. Likewise, when Armand meets Desiree, he falls in love with her and doesn't care that no one knows where she came from. When this phrase is used, it is in the context of Armand not caring about her name because his own name is from such a respected name. His was one of the "oldest and proudest in Louisiana." Later, when the child they have appears to have African American characteristics, Armand automatically blames Desiree since her heritage was unknown. Faced with a mixed race child, Armand now very much cares about her name because he blames her for the child's appearance. Of course, the irony in the story is that it is Armand's family that contains blood of African heritage.