You have to file a Petition for Name Change. An attorney may charge you according to his or her estimate of how long it will take to prepare that petition and have the Court approve the name change at a hearing. Some attorneys may charge you a flat fee. In addition to the attorney fees, the Clerk of Court will charge you a $401 filing fee to start the petition.
You don't strictly need the father's permission, it's still up to the judge. However, the law requires that you notice the father by serving him with a copy of the name change petition, and the father has the right to object.