Murtagh worried that neither Eragon nor Nasuada had spoken in his defense after the war because his reputation had not seemed to improve at all. He even confronted Nasuada about it, and this part from earlier in the book backs up her answer that she was telling people the truth about Murtagh but that it can take time to get the word out and change people's minds:
Regular folks may not have heard Nasuada's defense of Murtagh, but those who are plugged into the political realm have. And her defense has been strong enough for them all to be aware that she is fond of him personally. It's obvious according to Carabel.
I'd like to imagine that when Murtagh first reveals his presence to Nasuada's court, he will expect shock and hostility, but instead he will be met with annoyed resignation. They will all just be thinking, Oh great, guess we're going to have to get ready to call this guy "your highness" soon.
