The article reports that "Only six states -- Georgia, Hawaii, Iowa, Massachusetts, New York and North Dakota -- have statutes establishing equal name-change processes for men and women when they marry." It goes on to say that "Couples who want to hyphenate or combine their names also must endure the lengthy court procedures in California. One of the more notable examples was Los Angeles Mayor Antonio Villaraigosa, who went to court to fuse his last name, Villar, with his wife's, Raigosa, when they married in 1987."
I actually had no idea. I've known plenty of different-sex couples who were married in various states not listed above who have hyphenated their names, combined their names, or changed both last names to a chosen name. In telling the story of how they decided on their family names, none of these couples mentioned having to go to court or pay any fees. This surprises me a little, given that many of the folks I'm thinking of are civil libertarian types who I would have expected to be vocal about the discrimination. But now that I think a little more about it, most of the couples I can think of are people with complex assets and routine dealings with attorneys, so it's quite possible that they just paid yet-another-legal-fee without pondering it.
The Massachusetts application for a marriage license had spaces for "name after marriage" for both parties prior to the inception of same-sex marriages. I don't know how far back this has been the case though.
When federal marriage finally happens, the forms in every state will have to look like the ones in Massachusetts, which have the same options for each person. So, really, federal marriage will benefit different-sex couples by giving them the option to easily and inexpensively have any names they choose.