Historically in the Western world, children take the same latter name as their parents. These names have many meanings and derivations. The meaning of these can be traced back, to a specific definition in most cases. A great many surnames trace their lineage back to the professions of their ancestors.
Even though most in most cultures surnames are the same as last names, following the pattern of coming last - in many cultures surnames are used first whenever addressing a person. This can be seen in Hungary and countries that have strong Chinese culture influence such as Japan, Korea, Vietnam, etc.).
According to specialists (Etymologists in particular), family names may fall under one of these categories:
1 - Given Names: simple patronymic names (Johnson)
2 - Occupational Names: describes the occupation of the first person to adopt such an name (Eisenhower).
3 - Location names: These are generic, although they may also imply specific locations. (Lucci)
4 - Nicknames: These usually include names with a description. (Schwartzkopf)
5 - Ornamental Names: These surnames are usually common among communities that were forced to adopt family names during the 18th and 19th centuries (especially Jewish families). (Reis)