When Della seeks out the place where she can sell her long brown locks, she finds the sign that says "Mne. Sofronie. Hair Goods of All Kinds." When she enters the shop, she sees the owner. The narrator describes her this way: "Madame, large, too white, chilly, hardly looked the 'Sofronie.'"
By adding "the" in front of Sofronie, Henry takes a subtle jab that tells us Madame Sofronie advertises herself as something she is not. First, a shop that sells "hair goods" caters to those who value external beauty and style. That Madame Sofronie is "large, too white" means she doesn't look the part of the elegant female she is trying to promote with her "hair goods."
Additionally, the fact that she is "too white" suggests that she is not the ethnicity that her name implies. "Madame" implies she is French, or at least European, but her fair skin color suggests that isn't true. When she speaks, her dialect also betrays her as fully American since she says "yer" for "your" and uses unsophisticated grammar: "Let's have a sight at the looks of it." She has none of the soft-spoken or rich accents and phrasing a foreign-born woman might have.
The fact that she is chilly—emotionally cool—is also ironic. A reputable shopkeeper should be warm, and "Madame Sofronie" elicits the expectation of heat and passion because of its exotic sound. Saint Sofronie of Cioara was a Romanian monk who battled tirelessly for the religious freedom of Orthodox believers in Transylvania. Madame Sofronie's looks and behavior have nothing in common with the monk's altruism. She takes Della's hair without acknowledging the great sacrifice Della is making.
With a few well-chosen words and an ironic name, O. Henry captures Della's unpleasant and uncomfortable interaction with the woman who purchases her hair.