I have been re-watching the Star Wars movie as to get ready for the Last Jedi and in the Force Awakens, Leia is introduced as Leia Organa. 

Is there a reason as why she chose to keep the Organa last name and not taking the Skywalker one? 

I know she has been adopted and raised by Bail and Breha Organa but I wonder if her decisions was only feeling based or for other reasons? The Organa name has probably more impact in politics than the Skywalker one but there must be a real reason.