If you changed your name, there should be an official document in your country according to which your name was changed to the one on your passport. You should try and obtain that document, submit a copy with the I-485 and keep the original for the adjustment of status interview.
It will only be an issue if you do not submit documentation of the name change.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.