Do I change my documents first or can I apply for my husband’s visa with my maiden name?

Although not completely clear from your question, I presume that your husband is a U.S. citizen, and that you entered the U.S. lawfully and with inspection. If that is true, then your husband could sponsor you in a marriage-based adjustment of status application in the Immediate Relative visa category, and this is true regardless of whether you already may have taken steps to have your passport and other documents reflect your married name. Of course, there are many other details with an impact upon eligibility for adjustment of status. It would be wise for you and your husband 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.