For Legal Permanent Residents ( Green Card Holders) , you would have to go to your country's consulate or embassy to modify the name on your foreign passport after a legal name change order is issued in a New York Court . Please check with your country's consulate to see if your country will accept a New York name change order to change the name on your passport before you petition for a legal name change order in New York. Some countries like Brazil will not accept an order from the State of New York. But most countries will accept it.
Christopher Tompkins is an Attorney that has been handling Legal Name Change Matters for over 20 years in New York City, Long Island, and Westchester. Contact him at 212 962-5363. Email: NameChangeLawyer@gmail.com. Visit his website at http://www.ny-legal-name-change-lawyer.com/