So here's the thing I always found interesting about human last names.
Traditionally, most family's just take the father's last name for the children and wife.
Doesn't that seem kind of antiquated? Imagine what if humans went by a different route way back in the past and it followed onto today.
Imagine if the children had both parents first name as their last names but with a hyphen seperating the two parents name?
It would be a unqiue way of naming and have a consistant way of passing down family heritage.
Some cultures do. You're referencing a patrilineal latinized heritage, which is what many Western people use for naming of children. But its not written anywhere that we have to follow those rules.
However, I have a friend who is of Indian descent (Tamil Nadu, to be exact) and his first name is a given name and his last name is his dad's first name. Since he lives in the United States now, he's told me that if he ever has kids he'll probably utilize the American custom of giving your surname to your kids, which would end that tradition (i.e., his kid's would have the same last name as him, as opposed to having his first name).
I had a professor in college who combined his last name with that of his wife when they were married, creating a brand new unrelated name. Their children also have that as their surname.
I have a friend who goes by her middle name (didn't like her first name, I guess). When she was married she legally changed her first name to her former middle name, her new middle name is her former surname, and her new surname is her husband's.
My mother is of Hispanic heritage, and when she married my father she legally dropped all of her extra last names. Interestingly, she had a lot of them, because her grandparents combined two family names to make one combined surname (so her dad had three family names), so my mom's birth surname was actually three different words, her paternal grandfather's dual name and her maternal grandfather's singular name. To make matters even more complicated, her first name is "Maria", which is an exceptionally common Hispanic name, so to avoid confusion among friends she went by her first and middle name. In total, she had 5 names, potentially adding a sixth when she married my dad.