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A family name is a name shared by people in the same family. Different cultures have different arrangements 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.
For example, Mary Brown married John Smith and she changed her name to Mary Smith. They had two children, David Smith and Kate Smith. Smith is the family name shared by the parents Mary and John, and their children David and Kate.
Some languages put the family name first. Some (for example Spanish) give both parents' family names in the childrens' surnames. In Russian most surnames change depending on the gender of the person (example: ...ski or ...sky for a male, and ...skaya for a female). Some, such as Javanese, do not often give anyone a family name.