Truth be told, patriliny does look a bit more Biblical than matriliny, as well as the concept of a woman as straight-out head of household seems to hold less water than man in that role. There are arguments against ‘patriarchy’, but not really any arguments in favour of matriarchy. Besides, emasculated men are little use to women anyway. Except maybe as masseurs or serving boys or some other such role.
Gee, thanks for this information, that Mexican husbands are emasculated because their wives don’t change their names to his when they marry. Never could have guessed!
Indeed, I know many Hispanic couples who are legally married, but have different last names. I think the only ones where the wife did change her last name are those whose families are very “Americanized” in other ways and so they decided to follow “American” marriage customs.
Marriage name-change conventions really don’t track parallel to matriarchy vs. patriarchy. Medieval Europe was certainly a patriarchal society, as was Tudor England, but I can think of many married queens who never changed their names.
Even Anne Boleyn kept her last name and did not become Anne Tudor, but I wouldn’t call Henry VIII “emasculated” at least toward the end of their relationship. (Certainly many would claim Anne had a lot of “soft power” over Henry at first since he was so desperate to bed her, but certainly the end of their marriage showed who
really had the power there.)
I also know that in many Asian countries, there are cases of a man marrying into a family that is of a higher status than his and changing his surname to that of the bride’s family. This was often done if the family lacked any sons to inherit. Rather than let their land, title, or family business go to some distant relative, they would find someone to marry their eldest daughter, take her name, and become a placeholder “heir”, and hope the daughter would have a son who would become the eventual true heir.
ETA: As to the actual question, I am a woman, but have really have not decided either way, and so far it seems this may never become an issue for me.

But I would certainly consider my husband-to-be’s wishes in the matter.