In the main quest line you are made the Thane of Whiterun. But I do not want to be Thane. Is there a way to be stripped of the title of Thane?
As you can read here, you can only lose your Thane status if the Jarl position is changed during a Civil War battle. Whiterun, specifically, you have to fight for the Stormcloaks to change your Thane status.