nordic is correct women must take the family name of their husband, but there is only one exception and that's if hubby is a foreigner.
Like in my case, wife is Japanese and she works in an ultra-conservative company, so she kept her last name. Having a foreign last name in her company would have caused confusion with co-workers and customers.. and other headaches
I guess if my wife worked at a mega international company, then it would be cool to have a foreign last name
Actually, you and nordic are incorrect. As the linked article says, "a Civil Code provision that requires one partner of a married couple, which in practice is
nearly always the female partner, to change his/her surname to that of the other partner"
The law was deemed constitutional because it is not sexist, because it specifically says that both partners must have the same name. That means one of them must change their name, not that "the woman must change", although as the underlined portion says, it is "nearly always" the woman who changes.
Some Japanese men do take the name of their wife though. Granted, it is rare and usually limited to situations such as the wife having no brothers to inherit the family business, so the newlyweds keep the wife's family name (with the intention of inheriting the business in the future).