In English-speaking countries, "first name" means your given name, ie the name your parents gave you when you were born. "middle name" is also a given name. "surname" or "last name" is the name you inherit from your parent (usually your father but sometimes your mother), which was also your parent's surname.
For example: my name is ChristineEllen Woodhams. Christine is my "first name" and it is what I am usually called Ellen is my "middle name" and only gets used on official documents Woodhams is my "last name" and is also my father's "last name" - his name is Roger (first name) Singen (middle name) Woodhams (last name).