A basic right we all have is the right to a name. According to the United Nations Convention of the Rights of the Child along with a name comes immediate inclusion in a civil registry and the right to a nationality.
Cultures have different ways of giving names to children. Those with a Spanish tradition, such as Mexico, tend to use given names followed by a first and second surname ("primer apellido" and "segundo apellido"). Foreigners in Mexico, especially those arriving from the North, frequently find it odd that parents do not have the same surnames as their children.
Mexican parents are free to choose their children's given-names but the registration process for surnames is strict. The newborn receives its father's first surname as its first "apellido" and its mother's first surname as its second "apellido". Hence, the surnames of parents are different from their children on government issued documents.
In Mexico a baby born in a hospital goes home with a birth certificate that registers gender, weight, length, parents' full names, place, date, time of birth, and a foot print. Parents or legal guardians are allowed a time period in which to register the baby's given-names at their municipal civil registry office. If that time period is exceeded then witnesses are required to accompany the parents or guardians and baby to the civil registry. Indigenous people frequently prefer to register their children's birth in what they consider "their" municipality, even if their child is born in a distant location.
In the Spanish system the first surname is the one used for putting names in alphabetical order. Next the second surname is alphabetized. Only then are the given-names used for alphabetizing. The frequent "security" question asked by U.S. banks, "what is your mother's maiden name?" would be senseless in Mexico -- it is printed in the phone book.
Latin Americans from Spanish speaking countries who move to the U.S. will frequently hyphenate their surnames so as to keep both their "apellidos" yet not be alphabetized under their mother's maiden name.
Names can get quite long, especially with multiple given-names. For the sake of shortening a person's name it is usually a given-name that is dropped rather than one's second surname. If an initial is used it will usually be for the second surname, not a middle name.
Under current civil registry rules a Mexican woman keeps her birth name for life. Though she may choose to take on her spouse's surname, frequently with the possessive "de" between her first surname and her spouse's, she keeps the name with which she was registered at birth on her government issued documents. Hence, in order to cash a check made out to her, she will need to have her name written as it appears on her identification document.
Mexican spouses who are active in politics or business will sometimes go to great lengths to use their legal names and keep their marriage out of the picture as much as possible in order to lessen talk of nepotism.
On a similar note, when noted politicians do not use a second surname and instead write their name with a middle initial, it will frequently be a tip-off indicating that their second surname is a non-Spanish or non-Indigenous surname.
Among Mesoamerican surnames, Maya names are more common in Mexico than those from any other Indigenous language. Nahuatl is a source of given-names, even among those who do not consider themselves Indigenous.
The United States cycles through trendy names that are popular for a few years and allow calculating people's age by their name. Latin America doesn't seem to go through those cycles. However there are names that are popular in some countries and not in others. A man named Jairo will likely be from Colombia or Venezuela and Rodrigo from Central America or Colombia. Xochitl, Xicotencatl, Netzahualcoyotl and Cuauhtemoc -- names of Nahuatl origin -- will be from Mexico.
A new phenomenon regarding names has evolved with the Internet. One would think that readers who comment about a newspaper or magazine article online would be among those who most want to be able to make a statement and be recognized for it. Yet they rarely use their names, much less their email address.
There are organizations where as a matter of policy, only first names are used in an effort to make sure participants stay out of the limelight. One such organization is the loosely organized Occupy Wall Street. Yet even so, some people can still be identified. A Harper's magazine article quoted from the speakers log at Manhattan's Zucotti Park and mentioned "Charlie from Cuernavaca" who delivered a greeting along with pericón flower-crosses from Cuernavaca for Liberty Park. I received several inquiries asking if I am that Charlie.
An archaic definition of surname is a name title or epithet added to a person's name, especially one indicating a location. It worked for me.