
Hummm
I don't know if this works in Asia in general... But I've read another manga like this too (it was Korean)
There was a rich guy and another orphan.
So that the family wouldn't separate them, the rich guy filed an adoption request so that the other would have his last name (since they couldn't get married).
I think this is strange for us who don't understand these types of processes.... (⊙…⊙ )
But I'm almost 70% sure that ending wasn't translated well...

Gay marriage is not legal in Korea, Japan or other major East Asian countries. The loophole for that was through adoption or fliling for a "legal heir".
Through adoption, same-sex couples (or families who otherwise can't marry but want legal rights), can do things such as: sponsor partner citizenship, medical decisions, share property, inheritance, etc... basically all the legal things that family members can do for each other.
Say for example your partner was in an accident, the hospital will call the family members (if any---and if not, it would go through government subsidiary funds); outsiders such as lovers or civil partners would NOT be contacted and would not have any legal decision making rights over their partner's health because common law is not a thing.
Adopted son? I don't get it.