A family name is a name shared by people in the same family. Different cultures have different customs for a person's family name and given name. In English, the family name is always at the end, and it is called a last name or surname. Children usually have the same family name as their father. A married woman usually changes her family name to be the same as her husband.
First/given/forename, middle, and last/family/surname with John Fitzgerald Kennedy as example. This shows a structure typical for English-speaking cultures (and some others). Other cultures use other structures for full names.