What is the surname?

Formerly, in ancient Greece, notable people were identified by adding the place of their birth to their names. For example Aristotle of Stagira (or Aristotle stagirite), Hippocrates of Cos.
In Latin culture, the person had a praenomen or proper name and nomen that identified his gens. The gens are the names of the first founders of Rome. In addition, it was customary for the person's nickname or nickname to be part of his name. Example: Marco (name) Tulio (nomen, gens Tulia) Cicero (nickname, “el chicharito”, since his mother was a vegetable seller).
The surnames current can have several origins:
Patronymic surnames. They are derived from the name of the father of the family line: Pérez (Pedro's son), Hernández (Hernando's son).
Toponymic surnames. They are those that refer to a place, place, or living being: Burgos, Toledo, Sierra, Olmos, Cordero, Plaza, Prieto, Rojo.
Surnames derived from trades. Ballesteros, Tejedor, Sacristán, Hidalgo, Herrero.
Descriptive surnames. Those that describe qualities or defects of those who gave rise to them: Bald, Bad, Thin, Hair, Aguado, Crespo.

The names and surnames they are not used the same way around the world.
In Spain and most of Latin America, people identify themselves by giving their first name, paternal surname, and maternal surname.
In countries such as Portugal, Brazil and the United States, the identification is Name, Maternal Surname and paternal surname.
In places like Russia, Bulgaria and Iceland, it is used to put the name (eg Dimitri or Irina) the patronymic, formed with the name of the Father and the suffix indicating son or daughter (the father Petrov, his sons Petrovich and Petrovna) and the family name, the surname (Dostoyevsky and Dostoyevska).
In Japan the person introduces himself by first mentioning his paternal surname, then his maternal surname and finally his name.