How should I fill the "First name" and "Last name" in a undergraduate research application in the U.S.?

How should I fill this information if I have more than one given name and more than one last name?

For example, if my name is Juan Eduardo González Rodríguez. I have 2 given names: "Juan" and "Eduardo", and I have 2 last names (The first one of my father and the second one of my mother because that how it is done in Mexico): "González" and "Rodríguez".

Should I only write:

First name: Juan

Last name: González

or should it be

First name: Juan Eduardo

Last name: González Rodríguez (or González-Rodríguez)