Why two "last names"?

Like most Latin Americans and Spanish citizens, my family name is made up of two words: Blanco (my father's "main" family name) and Rodríguez (my mother's "main" family name). The two combined (with a space in between and no hyphen) constitute my legal family name. Nonetheless, it is customary to simply use the first family name in most day-to-day matters. So when growing up, my teachers would refer to me simply as "Saúl Blanco."

What should we call you?

Either "Blanco" or "Blanco Rodríguez" is fine. What you should never call me is "Saúl Rodríguez" or "Saúl B. Rodríguez", since my "main" family name is "Blanco". To avoid confusion, especially when being listed alphabetically somewhere, such as papers and conferences, the word "Rodríguez" is sometimes ommited. Sorry mom.