In this case I personally would leave it as Surname and put the two on the same line. If you really need to translate it, then use Second Surname as you would second or middle name.

In English surname is used and understood for English single or double-barrelled names.
In this type of document, I woud use
surname.
If you wanted to refer to the person's second rather than their first surname, then you could say "second surname" but normally you would just say suranme.
Good luck.
Sarah.

That way, Spanish people, who have two surnames, will put both, while those of us who only have one will not be too confused.

In American English, we are given only a first, middle and last name (we rarely call it a surname). Some people are given their mother's maiden name as a middle name, which can be confusing. But I believe in Spanish the second last name refers to the mother's maiden name. But often, Latinos in the US will use a multiple last name, with both last names.

Most forms we fill ask our second name.

I'm agreeing with another responder, but I wanted to give further explanation. If the contract has blank spaces for providing a "primer apellido" and a "segundo apellido", these can be combined into a single space for "surname(s)". This modification will make the contract usable for persons who use either one or two last names. Either situation can arise in either Anglo-American or Hispanic cultures, but as has been pointed out, single surnames are more common in the former, while dual surnames are more common in the latter. If the contract does not lend itself to this solution, you might just put "if any" after "second surname", thus avoiding the problem most English-speaking people would have in trying to come up with a second last name.

The problem with "mother's maiden name" is that this simply does not function as a surname for most of us in the English-speaking world, but is typically a bit of supplementary information used to identify us for legal purposes or for security. For instance, I give this information to my bank to access a teller over the phone, since it's consider virtually "secret" information.