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Wiktionary says "...has negative connotations among Overseas Vietnamese communities, as the word is associated with reeducation camp forced registration drives following the Vietnam War" and suggests "ghi danh" as an alternative.
Not really. People (including ex-refugee/concentration camp prisoners) use it all the time in normal conversation, such as to sign a receipt or letter, etc. without notable negative connotation.
Reported "She does not want to sign."