The name change would be time consuming. I suggest you wait until you are ready to be naturalized. At that time, it would be easy for you to change your name. However, if you need to change at this time, you need to really change your name under the local jurisdiction and without knowing it I can just give you general information. You have to file papers for name change in the appropriate court along with a court fee. Also, you need to print a legal notice in a local newspapers for at least 4 weeks.
Only see a licensed attorney before you make any decision. This answer may not be perfect in any given situation.