What is the origin of women changing their name to their husband's?

Answer 1

In laws of many countries, women were considered possessions, like cattle and chickens. Men also wanted to own the children (often for purposes of working in the fields), so they wanted the children of that woman to have his last name.

Answer 2

I am not sure but I think it had something to do with dowry rights. So if a man gave his daughter hand in marriage her children would have the right to the fathers inheritance if he were to pass away.