Yes, but in most places you'll have to get a court order to do it. Some couples want to be known by a hyphenated combination of their last names, and a few even make up new names that combine elements of each. For example, Ellen Berman and Jack Gendler might become Ellen and Jack Berman-Gendler or, perhaps, Ellen and Jack Bergen. You can also pick a name that's entirely different from the names you have now, just because you like it better. In the past, it was relatively easy to make all these changes simply by consistently using your new name. Today, you will need to go to court to get an official order changing your name to anything other than your new spouse's last name. Your department of motor vehicles will likely make post-marriage name changes to only one of the names that's on the marriage certficate, or, in some cases, to a hyphenated name that uses both.
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.
If you and your same-sex partner marry in any of the states that allow it, or register as domestic partners or civil union partners in the states where those relationships are equivalent to marriage, then in theory, one partner should be able to take the other partner's name.
For complete information regarding the status of same-sex relationship recognition, see Same-Sex Marriage: Developments in the Law.
The change should be recognized by the state department of motor vehicles and, according to the Social Security Administration, by the federal government for purposes of your Social Security card and passport. However, in reality, some same-sex couples have had trouble getting their name changes approved after marrying or registering. If that happens to you, keep going up the chain of command until you find someone who's familiar with the law and procedures in this area.
No. When you marry, you are free to keep your own name or take your husband's name, without a court-ordered name change. In most states your husband can adopt your name, instead, if that's what you both prefer. However, in general you'll need a court order if you and your husband both want to change to a different name that you share. Give some careful thought to what name feels best for you. You can save yourself considerable time and trouble by making sure you are happy with your choice of name before you change any records.