Because the FL didn't allow for the side chick to be included in the Orsia family registry. One of the first things she changed from her past life. FL is the one who has control over that cause she's the only heir to the Orsia family with their blood. (Her father married into the family) So calling side hoe with the Orsia family name as opposed to her original Baron family name means that they're either belittling FL's decision not to include her in the family registry or some snake somewhere (maybe the douche dad) has added her to family without permission. Basically, FL's fam is in a higher position than side hoe's orginal fam.
It's been a while since I last read this so I forgot the relevance of the surnames. Can someone please explain to me why calling the side chick that was such a big deal?