Spanish translation: Número de la Seguridad Social (NSS)
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SSN does not only exist in the USA, in Spain, we do have a SSN and we call it NSS (Número de la Seguridad Social) I do not know in other countries in Latin America or elsewhere in Europe. What I said about the BrE was that maybe the original text was written in the UK and it referred to something in Europe.
I think we should translate it to Spanish, because the SSN is not an institution, the same way we translate ID (Identity Card) as DNI (Documento Nacional de Identidad) even if in the UK, for example, citizens do not have IDs.
Hope this helps!