If the divorce decree does not state it, then you will probably have to apply to the court for a name change.
Each stage has its own rules for doing so, but in NJ you file a complaint, and publish in a local paper your intention. Then there is a court hearing because the judge wants to make certain you are not doing it to avoid debts or criminal charges. Once you have the court order, you send copies to Social Security, your state's DMV, etc. You can do it pro se or hire a lawyer to walk you through the process.