No creo que hay un equivalente en EE.UU. Yo dejo las siglas C.U.R.P. y en paréntesis su traducción literal.

Espero te ayude.

In Mexico, "Clave Única de Registro de Población".

Lots of references of this type being referred to as 'unique:

e.g
Puerto Rico:

State (St): Puerto Rico has its own unique code. In addition, several unique codes are used to identify nonresidents of Puerto Rico.
http://www.nber.org/mortality/1999/docs/4TERRGEOINT99.txt

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Note added at 2 horas (2008-07-29 07:04:03 GMT)
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“That means the child won’t be able to get a Unique Population Registration Code,” the equivalent of a Social Security number, Bulos said. The code is derived, in part, from the first letters of a person’s given name and surname.
http://articles.latimes.com/2007/may/02/world/fg-names2


The General Population Act regulates the National Registry of Population and Personal Identification. [21]The purpose of the Registry is to register all persons making up the country's population using data enabling their identity to be certified reliably. The aim is ultimately to issue the citizen's identity card, which will be the official document of identification, fully endorsing the data contained in it concerning the holder. [22] When a person is incorporated in the National Registry of Population, an identification keyword [23] shall be assigned to the citizen (Article 91 of the General Law of Population (Ley General de Población)). This keyword is used to register and identify Mexicans on an individual basis. That identification has the particularity of conferring a **unique code** for each citizen with which one can have direct access to multiple personal data. A unique code increases the risk of file interconnection. [24]
http://www.privacyinternational.org/article.shtml?cmd[347]=x...

http://www.proz.com/kudoz/spanish_to_english/law_general/608...
These are both in the glossary already:
Registration and Personal Identity Code
... or something along those lines.
It applies only to people born in or after 1982. (See www.consar.gob.mx/SAR/circulares/c39_1.pdf
This is the translation suggested on the web site below, about Mexican laws in English.
CURP: Individual Identification number

CURP: Clave Unica de Registro de Población (Single Population Registration Code). DGAE: Dirección General Adjunta de Epidemiología (Subdirectorate General ...
http://www.who.int/healthmetrics/library/hmn_his_mex_legalfr...

CURP. Clave Única de Registro Poblacional. (Single Population Registration Code). EFTPOS. Electronic Funds Transfer at the Point of Sale. FOBAPROA ...
http://www.whcri.org/PDF/report_mexico.pdf

My 2 cents...

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Note added at 1 day16 hrs (2008-07-30 21:00:56 GMT)
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This one from Harvard:

that would include the Single Code of Population Registration (CURP), the introduction of. 130. The Diagnóstico was published in 1995, and it wanted to ...
http://www.hsph.harvard.edu/ihsg/publications/pdf/lac/Mexico...