A name change is not required and does not make a difference in the immigration process.
No need to change names. USCIS will not consider a name change to have an effect on the application.
Based on your question, it appears that you should consult with an immigration attorney about the "change of status petition" that you mentioned. An immigration attorney will help you to go over everything, make sure there are no issues that could result in some serious problems and consequences, and give you the best chance of success. Good luck.
(734) 369-3131. This communication does not establish and attorney-client relationship with the Law Office of Michael Carlin PLLC or any individual member of the office. Confidential information should not be sent through this form.