The law is gender neutral in theory only as it is a fact 95% of women take their husbands names. We all know that tradition, peer pressure, societal expectations, etc, can force individuals to make choices in order to 'keep the peace' and not because they actually want to. It may satisfy the 'equal sexes' in the strictest letter of the law but let's not kid ourselves, this is not the lived experience of most women.
Divorce
And then there is the constantly recurring debate about the sanctity of the 'nucleus family'. Divorce rates are on the rise in Japan with 1 in 3 marriages ending in divorce. When everyone is on the same koseki with the same name, what happens when people divorce? Usually it is the mother who keeps the children and, as she has previously changed her name to be on her husband's koseki, she now has to change her name back. And because of this, her children also have to change their names as they are now on their mother's koseki.
Is this not serious disruption of the children's lives, that they now have to change their names because their parents decided to split up? Perhaps even suffer prejudice or bullying by peers in school because of it?
Privacy
It is true that some companies allow people (women, mainly, as we have established) to use their maiden names in a professional capacity. They are still, however, required to use their official names in certain settings and are, as such, forced to give that name to the company. So when their surname changes, they are divulging that they have married, whether they wish to disclose that information or not. Similarly, when they divorce and revert to their maiden name, they are publicly announcing this fact.
But let me answer your question:
Yes, I believe they should. Amend it to follow the times. I have spent the last 8 years as a systems developer for the Danish government and systems here change all the time, to lesser or greater extents. When the people, the population change, the systems follow these changes.
- When gay marriage was introduced, we changed the systems to reflect this and not just have one of the men written in the 'wife' column.
- When it became possible to change your gender, we allowed for the change of social security numbers since these the numbers in it reflect your gender.
- When people from other countries come here, whether permanently or for a period of time, say, to study, we made it possible for them to get a Danish social security number, because that way we can store things like medical information, certificates, degrees, and such on equal footing with Danish citizens.
I have many more examples but I'm sure you get the gist. My experience tells me that just because something is hard and difficult
doesn't mean it shouldn't be done.