What does the baby’s lack of a name indicate?

You are referring to Desiree? Desiree's lack of a name reflects the fact that her family heritage and background are unknown. Historically, a person's name spoke to their social class and prestige, in addition to showing if a someone's background included any ancestors who were black.

Monsieur Valmondé grew practical and wanted things well considered: that is, the girl's obscure origin. Armand looked into her eyes and did not care. He was reminded that she was nameless. What did it matter about a name when he could give her one of the oldest and proudest in Louisiana?