You will need to apply for a name change with your local court. After the court has given you an order allowing you to change your name, you will need to submit that order along with a new application for employment authorization (I-765) to USCIS to get a work permit with your new name on it.
You would should inquire with your local state court clerk who can likely inform you on the name change procedures. Once you change your name with the state court you would then be able to inform immigration of your new name.
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