If a transgender person applies for a DBS check, they are just as obliged to disclose their previous names as anyone else is (no different to a married woman having to disclose their maiden name etc) and you sign to say you understand that. Many also do consent to their previous name being declared on the certificate. *If* they have convictions under their previous name/declared sex, they are published on the certificate. Even with a change of name, someone can still be matched to a criminal record via National Insurance number, previous addresses, DVLA/passport info etc.