Although the specifics of the process may vary a bit from state to state usually legally changing your name can be done with only a serious of forms. Some states will require you to go through the court system while others may make it as easy as getting the required forms online.
Most commonly these forms include a petition to legally change your name, an order that shows cause for legally changing your name, and a decree to legally change your name. In most cases after these forms are filled out it is as easy as taking them to the court clerk, paying the associated fee and filing them.