Hello Ma'am. You are not required to change your last name in order to please the immigration service. This is a personal decision which only you have the right to make. In order to adjust your husband's status to a lawful permanent resident, you must file a marriage petition along with supporting evidence of the bona fides of your relationship. You must further have him file his application for adjustment of status. Please be sure to have all grounds of ineligibility reviewed by an immigration expert. The attorney is useful in not only preparing the applications and working with you in gathering the evidence but also in preparing you for and representing you at the interview. Best regards.
No, there is no status for you to change, you are a U.S. citizen for life. Whether or not your out-of-status husband is eligible to adjust through you is a whole other question. Consult with an immigration lawyer.
This information is not intended to create an attorney-client relationship, as the information provided is extremely limited and without the benefit of having all facts available.
You may want to change the name on the Social Security Card and on the driver license. The information how to make the changes are at the links below:
I agree with my colleagues that you may petition for your spouse. I would strongly recommend to have an attorney to assist both of you to file the family petition, application for adjustment of status , application for employment authorization, application for travel document and all supporting documents to prove your bona fide marriage and your husband's eligibility for green card. Submitting forms not completed properly and failing to submit all necessary documents will cause unnecessary delays to your case.