Ugh, I'm disappointed too.
I've waded into this debate many times so I'll try to avoid getting massively sucked in. But when a woman changes her name to her husband's, it is unequal - how on earth can it not be? One person's name gets to stay and be the name of the family. One gets ditched.
However much the woman feels she is, or in fact is, making a free choice, when she does that she is reflecting and perpetuating the deep-seated, often not necessarily even conscious, idea that men are more important. She doesn't have to consciously think men are more important. Whatever she thinks, that is the message she's sending - to her sons or daughters, to her pupils, to her colleagues, everyone.
And that is how the message of inequality gets passed on (among a million other ways). Why does that matter? Because deep down inside men and women, that inequality of value is what allows other, worse, less symbolic, more real inequalities to perpetuate. Like the shocking levels of male on female DV and abuse, boys' attitude to rape, unequal pay, unequal shares of housework etc etc that hold women back, hurt women, keep women in their place. Those things happen because more value is placed on men and deep down men and women know that, and that is what feminism should fight. If you are a feminist I don't see how you can be happy with perpetuating that unequal message, however symbolically.
If that wasn't the case, and it was 50-50 men taking women's names too, I wouldn't think it was sexist (though I personally think changing your name is a ridiculous, pointless and outdated hassle and something I would never do).
But it's not like that, is it. It's almost exclusively women who do it.
And it's often not a free choice anyway. Women often do it because they are worried about being seen as strident ballbreaking feminists, because of pressure from family, because their groom mopes and complains if they propose not doing it. I've seen strong, professional women who would do better to keep their names cave into that pressure, even when they didn't really want to. No, that's not coercion or force, but it's not a fair, free choice either when that pressure doesn't apply in the other direction.
If it doesn't matter, ask yourself what percentage of men you know would be happy to do it, and why that percentage is so small? If it doesn't matter, ask yourself if it would be OK if every time a black person married a white person, it was traditional and expected for the black person to take the white person's name, because traditionally white people held all the power, and 90% of black people just happily went along with that? Would they do that?
Of course it matters and IMO she is doing us all a disservice by sending out an unequal message. Of course it's her "choice". But feminism does not equal any old choice. Feminism is about equality.