You can have all your documents in your new name (DL, SSN. and banks and credit cards) and still have your green card in your old name. Just dont update your passport, will be tough to travel back to the homeland. We kept all the immigration and passport in my wifes maiden name while changing ssn, bank accounts DL to her new name. When she appliwd for citizenship she changed it all over to married name and got her new passport in her new name. Not necessary to change your name with USCIS.