How to refer to a 'second' last name or family name?

I know in most english speaking countries, there's no such a thing like a "second" last name. But for example in spanish it's quite common (we are fond of long a complicated names lol), our full names consist on usually two names (even more!) and almost [always][1] two "last names". For instance:

Pedro Arturo Rodríguez Loyola
^ first name ^ last name
      ^ middle name    ^ ????

"first last name" it's the father last name and the "second last name", it's the mother's maiden name (women doesn't lose their last name when they get married). This is giving me some headaches when trying to model data for patients name, since I want to pick something that will make sense to developers of countries different from mine.

[1]: rarely some people have only one.

Dr. Manuel A. Pérez Quiñones (archived version), a computer science professor at Virginia Tech, seems to have some personal experience with this. He calls it simply the second surname.

He also writes at length about the incompatibility of the human and computer handling of the Hispanic culture's two last names.

After looking over what he has to say on the subject, it suggests to me that there is no accepted or typical way for handling two last names, at least in the U.S. He also doesn't indicate that there is a common way for referring to the second last name.