You cannot change your name now. It is too late for you to change name on green card. You should have done that when you filled out I-485 form. Like the first answerer did. You now have to wait till you apply for citizenship. When you fill out N400 form for naturalization, you should put new name. Or you can file change of name petition with local court. But I will not suggest you to do so because it will be troublesome when you show legal documents with different names on it. You will have to bring the court order of name change all the time to prove it is the same person with 2 different names.