Hispanics usually have two last names or “apellidos.” The first surname is their father’s surname (known as the “apellido paterno”), and the second surname is their mother’s maiden name (the “apellido materno”). Some examples:
Juan García Reyes
or
Juan García y Reyes
Carla Rodriguez Calderón
or
Carla Rodriguez y Calderón
http://www.spanish411.net/Spanish-Hispanic-Names.asp
I see nothing wrong with this long standing custom.
Yes, but the first surname is the one they consider the real one. If they simplify it to just one for whatever reason, like writing their name in a sign in sheet or something, the fathers is the one they use.