formality - Confusion over “family name” in English: What about double-barrelled last names?

How do you fill out an official form in English that asks for just one last name when you instead have a surname which comprises more than one word?

I currently live in a Latin country, where we have names which have “two last names”. One of these “last names” is the father’s surname and the other is the mother’s. The order can vary between countries and even individuals. Sometimes you see these written with a hyphen or an “y” to connect them, but sometimes you do not.

For example,

I am filling a DS-2019 Form because I am moving to the U.S., but for the name they ask for

_______________    _______________        ________________    
  (Family name)      (Given name)          (Middle name)

That may map well to someone with a name like Franklin Delano Roosevelt, where you have one one given name, one middle name, and one family name (and in that order), but what about when you have more than one of one of those, like George Raymond Richard Martin, George Iain Duncan Smith, or Federico del Sagrado Corazón de Jesús García Lorca? Put them both — or all — in the one field? Invent new fields?

So, given the Latin name (with two last names), how do you fill this field? My last name has two names, so do I give them both, or choose just one, or hyphenate them, or something else like using one of the two last names as the middle name?

So under the last idea, the answer will be

____Perez_______    _____John_______        _____Espinosa___    
  (Family name)      (Given name)            (Middle name)

Answer

The easy parts are the first and middle name. First name, obviously, would be "John", and the middle name would be any middle name the applicant may have.

The tricky part is the last name, and is a problem for a lot people coming from Spanish-speaking countries (I don't know at all about Portuguese). My understanding is that there are two options which are primarily used.

Option 1: Hyphenate
In this case, the applicant would list the last name as "Perez-Espinosa". It's cumbersome, yes, but it includes the entire name.

Option 2: Single name
The English-speaking cultures' tradition (I don't know of any exceptions) is that a person's last name is their father's last name. The Spanish-speaking tradition is that both the father's and mother's last name is applied. According to this website, the father's name is the one that is listed first and passed down to future generations (good thing I checked, I vaguely remembered it being the other way around). The option I'm getting at here is to list simply the name from the father (Perez in this case).

I know that both of these options are used by immigrants to the US from Spanish-speaking parts of the world, and I believe that which option is used is based on personal preference (although I may be wrong on that part).