In some countries compound surnames are the norm. The entire compound surname goes in the surname field.
English speaking countries, Americans in particular (BTW: I am American), seem to get rather confused about compound surnames. If there is no hyphen, which is usually correct, the name can get turned into a middle name, last name situation. The solution being to incorrectly add the hyphen.
For people immigrating from Latin American countries to the US, the second, or maternal, surname sometimes gets moved to the middle name position.