User blog comment:Xilinoc/Ch. 598 - The Shooting Star Project (We Only Have To Beat You Mix)/@comment-11446176-20140926091423/@comment-24577094-20140928170636

Xili's right. It goes according to social status. If the husband has higher status, the wife takes his name. But if the wife has higher status, the husband takes her name. Isshin abandoned Soul Society, gave up all his power, and had no home, and no money. Masaki was from a noble family with power, money, and a home. Pretty clear ranking. Although, that's the more traditional approach, and I'm not sure what the modern ruling is.