Because, and I'll quote from article, "she signed her name on the back of the ticket shortly after winning, and altering the signature would nullify the ticket." That is, she could have formed an anonymous trust, but now it's too late.
This is completely unrelated to the question you're supposedly responding to. Some people are advancing the argument that it serves an important societal interest to publish this woman's name. Specifically, it builds trust in the lottery by publicizing that somebody won.
bachmeier is pointing out that you could accomplish this equally well by making up a name and publishing it as the lottery winner. The fact that somebody signed a ticket has no bearing on that.
