Names are usually given by parents for identification. Moreover, the last name is the name common to all members of the family. It is a name bore by the father, mother, children, and probably some members of the extended family. The last name is usually referred to as surname, and it usually comes last after the first name in the western culture. Nevertheless, some other cultures choose to put the surname, which is the last name first, before the first name.
On the other hand, your first name is the name which you primarily answer everywhere, either among or outside your family. It is a name given to you during birth or baptism; this name is uniquely for you alone of all other members of your family. The first name usually comes first in western culture, but the other way round in some other cultures like the Chinese'. In addition, the first name is usually used in an informal gathering, while the last name is mostly used in a formal gathering.