In English speaking countries (US, UK, Australia), people usually have two given names (first and middle), and the family name goes at the end, which is why it's called a [last name]?. The last name is usually the last name of the father (and the mother, because it's usual for the wife to take the last name of her husband as her own), but sometimes is the mother's, or a hyphenation of both parents' last names, known as a double barrel name. Other countries where this is the case are France, Germany, and Poland.
In Spain and countries of Hispanic culture (former Spanish colonies), each person has two family names: the first is the first family name of the father, the second is the first family name of the mother. Like in the case of the English-speaking middle name, the second family name can be omitted or reduced to the initial.
In other cultures, like the Chinese and Hungarian, the family name is actually put in front of the given names. So the concept of first name and last name only applies to some cultures and it causes total confusion in many non-English cultures. In many non-English speaking countries, names are refered to as surname and given name to avoid ambiguity. Many Chinese people add a Christian name in front of their Chinese name, so an example would be is Martin LEE Chu-ming (chairman of the Democratic party in Hong Kong). The surname is often written in ALL CAPS to avoid being mistaken as the middle name.
In other places like Iceland, there is no real family name; the last name of a person is a modified form of the first name of the father (a patronymic? custom). Similiar customs exist in some parts of India. However, many Indians (from India) living in English-speaking countries give up on this tradition because many English-speakers so consistently misunderstand the custom; therefore many Indian fathers simply follow the English-speaking custom to pass on their last name instead of their first.
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