A spouse who wants to take the other spouse's name upon marriage should promptly begin to use that name. Use the new name consistently, and be sure to change your name on all of your identification, accounts, and important documents. To change some of your identification papers -- your Social Security card and driver's license, for example -- you'll need a certified copy of your marriage certificate, which you should receive within a few weeks after the marriage ceremony. Take the certified copy to the Social Security office and the department of motor vehicles and ask them to change your identification documents.
If you live in California, see How to Change Your Name in California, by Lisa Sedano and Emily Doskow (Nolo), which provides step-by-step instructions and all the forms you need to change your name.