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.