Can I petition my mom even though she is still using her first husband's surname?

Generally, a naturalized U.S. citizen may sponsor a parent for immigration in the Immediate Relative visa category, and this is true regardless of the use of different surnames. As you may expect, it will be necessary to provide documentary evidence of the relationship and additional scrutiny may be applied when there is a complication about surnames. It would be wise for you and your mother to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options, and strategies to attain your goals, and who then could offer legal representation in the often complex application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.