I wonder if I'm less confident with cooking partly because it's like, failing at cooking means being unfeminine, a bad wife, etc.?

Oh, I hadn't thought of that. I always have the knee-jerk reaction of refusing to do anything people expect of women/wives/girls. I decided very early on that gender stereotypes are not for me... but of course there are people whose expectations I respect and try to meet, they're just not gendered expectations. :)

Yeah--some Koreans in Japan adopt Japanese names officially, others have their Korean names on the paperwork but use Japanese names in daily life for convenience/safety.

Thanks for that glimpse into something I know absolutely nothing about.

I think people used to do that here, too, take names that sound more domestic, but nowadays there are so many foreigners that you don't blink at it anymore (and I like that).