Back in the medieval ages when a woman was married to a man, they were basically considered property for my understanding and treated like an extension of the man’s person and family. So it was customary for women to take the man’s last name since they were being joined to his family. But now here in the 21st century women are fully independent and last names don’t really seem to mean much of anything. I mean what is Smith or McGregor or any last name really mean anymore? Especially in the digital age, lots of people have digital usernames like SarahSmith1727373. So the last name clearly doesn’t mean much anymore… Which leads me to wonder, why do the majority of women still take the man’s last name? Especially when some of them have a horrible last name? I have seen some butt ass ugly last names recently, like Fink, Weimer, Slotsky/Slotsky, Hiscock (no joke this is a last name), Hardman… And then you hear the woman’s name and it’s like something way more reasonable and less stupid sounding like Kingman, or Harrison, Walls, etc.
In China you simply keep your birth name forever, and children always follow the paternal side. That’s why having a male hair is important there, because a woman will only bear offspring for her spouse’s family.
As to why the family bonds are so strong, it’s part cultural (your elders are always right and must not be criticised, and you must take care of your blood above anything else), part societal - parents work too much (60-100h weekly), so children are generally raised by their grandparents, which strengthens the bond across generations. And because the pension system is totally insufficient, grandparents will at some point typically move in with their kids, so people are used to live in a multi generational household.
By the way, China is just one example, there are even Western countries where it’s not possible to change the names, such as Luxembourg.