Spanish citizens (and most of latin-american) officially have two surnames. Your first surname is your father's first and your second is your mother's first. Women do not change their name when they marry. This seems to imply women's equality with respect to names, but it does not. You use your two grandfathers' surnames and forget your two grandmothers'. (Of course, the law allows parents to switch the surnames of their newborns, but most people don't do it).
Unofficially, the sequence of surnames is infinite. You have your father's second surname as your third, your mother's second as your fourth, your father's third as your fifth, and so on. My sequence up to the sixteenth term is Santos Leal Corchero Villalba Herrera Ramos Ponciano Rebollo Martín Vallecillo Gallardo Guillén Suárez Cabezón Pavo Fernández.
A more balanced choice would have been to take as your odd-indexed surnames those of the parent of your same sex. But then, how does the infinite sequence behave? Answer: for each power of 2, your first 2^i surnames are the first surname of your 2^i ancestors in the i-th generation, ordered according to the following self-similar sequence of sexes (a is your sex and b is the opposite one):
In case you did not notice, the first half in each row equals both the odd part of that row and the previous row. The first and second halves of a row are opposite to one another, as are the odd and even parts. Even rows are symmetric under middle reflection and odd rows are antisymmetric. The infinite sequence obtained is known by combinatorialists as the Thue-Morse sequence.
By the way, Leal means loyal.
Q: So, should we call you 'Francisco Santos' or 'Francisco Santos Leal'?
A: Whatever you prefer. What you should never call me is 'Francisco
S. Leal', or take 'Leal' alone as my surname. Even in Spain 'Santos'
would be considered my main surname, although both 'Santos' and 'Leal'
will appear in every official document. In my research papers I use
only 'Santos', partly to avoid this sort of confussion but partly also
because that is what I use in my everyday life. See, e.g., my email
address. Other people use both their
surnames, sometimes joining them with a dash. And some people
prefer to be called by their second surname. (This tends to happen
when the first surname is a common one and the second one is not, like
in 'Rodriguez Zapatero').
In case of doubt, you can always call me Paco!