A formal change of name (by deed poll, by marriage, by court order, by adoption) updates the name on a passport, on a driver's licence, on a bank account. It does not, in any jurisdiction the desk knows, update every identifier attached to the person. Certain identifiers are administrative artefacts of the body or of an early identity assignment and they persist regardless.

The national insurance number, the social security number, the tax file number, the personal identification number used by some governments: these are typically assigned once and kept for life. The name attached to them may change; the number does not. A record that uses the number as its key (a tax history, a state pension history, a healthcare record) is therefore preserved across name changes.

Date of birth, place of birth, and mother's maiden name are not numbers but they are effectively identifiers in many systems and they do not change. A reasonably confident match between an old identity and a new one can be made on the basis of date of birth and one other anchor.

Biometric records (fingerprints in jurisdictions that collect them, facial templates where they exist) are not affected by name changes at all. The identifier is the body, not the document.

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The desk reads the picture of a person under a previous name and a current name as continuous, because the underlying record is. It works with clients on what surrounds the name change in the public record, since the name change itself cannot ordinarily be hidden from a determined search, but its surrounding visibility can sometimes be considered.