The example for today is a wife taking her husband’s name. There are many functional, traditional marriage cultures where this is not a requirement. Some cultures practice hyphenation to demonstrate two families melding into one, rather than taking the husband’s name. Others use taking the wife’s name to represent the wife granting her husband authority over all that she possesses. The problem is not with a wife taking her husband’s name, the problem is that it is quite ridiculous to take a practice that is not universal to the practice of patriarchy and extrapolate that it is (or about as bad, that it is the most superior patriarchal approach, also untrue).
Conservatives in America, which is where I live, would do well to stop committing this ridiculous fallacy all the time about loads of other things, although the married name one is a chronic offender across the conservative spectrum.