In most states, you can request that the judge handling your divorce make a formal order restoring your former or birth name. If your divorce decree contains such an order, that's all the paperwork you'll need. You'll want to get certified copies of the order as proof of the name change -- check with the court clerk for details. Once you have this official documentation, you can use it to have your name changed on your identification and personal records.
If your divorce decree doesn't contain an order restoring your former name, check to see if it can be modified to include language restoring your name. In some states, this is possible even after the divorce is final. For example, in California you would use a form entitled Ex Parte Application for Restoration of Former Name After Entry of Judgment of Order (FL-395).
Even if your divorce papers don't show your name change, you may still be able to resume your former name without much fuss, especially if you still have some proof of that name, such as a birth certificate or old passport. In most states, you can simply begin using your former name consistently, and request that it be changed on all your personal records (see Changing Identification and Records).
If you're returning to a name you had before marriage, you're far less likely to be hassled about the change than if you adopt a completely new name, but you may still face some bureaucratic barriers in returning to a previous name. This is especially likely if you are a recent immigrant or do not have reliable documentation of your former name.