Isshin Shiba/Kurosaki

I always thought that Isshin's last name was Kurosaki but I learned that it was actually Shiba. Normally when a couple gets married the wife takes in the man's last name. It should be Masaki Shiba and everyone in the family shouuld have the name of Shiba instead it is Kurosaki. When did Isshin decide to take in the name of Kurosaki as his last name?

Minato Namikaze + Kushina Uzumaki = Naruto Uzumaki.

Give a quick read, maybe the Mukoyōshi link too.

The standout lines are about the male being adopted into the females family, and thus namesake, if there's some significant lineage reasoning.

In Naruto's case it fits well given her side, besides Minato not taking the name. Less so for Bleach unless we assume Isshin is valueing humans over himself (likely with his power dump) and wants the family to grow up a part of that side, not his.