It's not that he can't legally change his name, but the article states that he doesn't want to take the time to fill out the paperwork or pay the fee, like other people have.
Some people want everything handed to them, and they don't feel like the rules apply to them. This is a case of narcissism and laziness rolled into one.
He's fighting it because in California, women who get married don't have to pay a fee to change their last name, they don't have to put out advertisements first and they don't have to go to court. All they have to do is present a valid marriage license and their name is changed. He wants the same right.