To reiterate what others have said, you can do whatever you want with your name as far as I’m concerned, but you can’t necessarily call it a free choice or a feminist one.
For couples that even give this any thought, one option comes with the weight of thousands of years of human patriarchal history behind it, the other is actually tainted by the ‘F’ word. It might technically be a free choice, but let’s not pretend that it’s between two equally weighted options.
That’s why only one of the two options can be called feminist IMO. It doesn’t make the other option wrong, but you can’t have your cake and eat it.
We all do all kinds of things everyday that reinforce the patriarchy.
My partner and I didn’t plan to get married - we only did so because we bought a house (which we didn’t think we’d ever be able to do), and marriage was the easiest way to tie our financial lives together in the way we wanted. It was a financial transaction essentially - which is actually pretty traditional when you consider the history of marriage!
When you strip away all the princess day gubbins, I do think that marriage is capable of shucking off the old patriarchal baggage, though the available wording in the ceremonies needs to be changed. We wanted to say “partner”, not husband and wife, but we weren’t allowed.