I have been re-watching the Star Wars movies 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 based on her feelings or for other reasons? The Organa name has probably more impact in politics than the Skywalker one but there must be a real reason.