There are many, many cultures around the world where not everyone in the family shares a last name. It's just because that is what you are used to that it seems like it ought to be that way. In quite a few European countries, it is actually illegal to take your husband's name, as the author noted. That's been the case in France since 1789 and they seem to have survived. According to Islamic tradition, a person’s name is always linked to that of their father and it is a sign of respect for a woman to retain that name even after she marries to indicate loyalty to her family line.

A name isn't what makes a family. My husband and I have different last names, and we've been happily married for over 30 years. Our son is just fine. It's all what you are used to and expect.