This is what theINE in Spàin calls it.
"The Municipal Register is an administrative register listing all the residents in a given municipality.
The Register will include at least the following information:
Names and surnames
Gender
Habitual residence
Nationality
Place and date of birth
National ID Card Number (Documento Nacional de Identidad, DNI), or the corresponding foreign national ID card number. For European residents in Spain, this refers to the number on the Certificate of Inscription in the Central Foreigners Register (Registro General de Extranjeros). In the absence of this Certificate, the register will record the number of the identity document or valid passport issued by the authorities of the country of origin.
The resident’s academic or school certificate or title.
Other information that may be required to draw up the Electoral Roll (Censo Electoral), in full compliance with the fundamental rights recognised in the Constitution."

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Note added at 28 mins (2023-02-08 17:26:48 GMT)
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As for the "situación" part, I'd probably use "status" (...to renew their municipal register status...)

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Note added at 29 mins (2023-02-08 17:27:48 GMT)
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"...padron (municipal register) status and will act as a quick way to use the free local bus service, library and other social services..."

http://euroweeklynews.com/2011/07/25/joaquin-albaldejo-deleg...

Short and sweet. It is used for the census and voter rolls. They also use it to find taxable individuals.