Wait until you naturalization. Thereis no extra charge for changing your name.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Better to wait.
Law Offices of Hasbini 619-200.8986. Free on phone and in office consultation. http://www.sandiegoemploymentlawyer.net
You are able to legally change your name when you file for naturalization. You write the new name you wish to use on the application form so it's fairly simple. The filing fee for naturalization is $680 unless you qualify for a fee waiver.