Japan annual births fall to new record low
apnews.com
apnews.com
But, really, women seeing having to take the husband's name as a reason not to marry? I mean, sure, that's rather restrictive for no good reason. But from where I stand, if you're thinking of marrying someone, and having to change your name is your reason not to, you don't really want to marry them very much.
(Easy enough for me to say as a male. But would I have changed my name to marry my wife? Absolutely.)
Additionally, without seeing how the polling was done, this option may be seen as better than more ‘selfish’ reasons.
If my assumption is wrong and they're instead thinking "I'd quite like that kind of marriage in general, but I'm not going to change my name", then there's an easy fix, as you suggest.
This is important for the official family register.
So not changing a name is literally not an option.
And in Japan, the land of paperwork, changing your name is a whole lot of paperwork and headaches.