You are incorrect asylee27. Asylees and greencard holders can change their names.
eddie_240 - it would have been easier for you to change your name before you got your greencard, as it would have cost you considerably less. Now you will have to go to court to get your name changed, and then send an I-90 application with a copy of the court decree (proof of name change) so you can get a new greencard with the new name. This will cost you the current price for the I-90 form. It is currently $290 plus $80 biometrics fee. Oh, and as part of the I-90 application, you will have to send in your current greencard.
I changed my name 3 years after applying for my greencard and submitted the court papers to NCS so they could update my pending I-485 application. I also applied for an new I-94 with my new name by filling out the I-102 application which was only $80 at that time. When my greencard got approved, it was sent with the new name.
Hope this information helps.