Some jobs may require an applicant to pass credit, criminal or police checks before they can commence employment. If an employer requires a list of previous names from all applicants as part of the employment process, then an employer can ask the prospective employee to provide previous name details. Such details can only be used for a legitimate purpose, such as verifying identity for background checks that the position may require.
A prospective employer cannot require a potential employee to provide previous name details, if such information is not required from other applicants. This may be grounds for a complaint of discrimination on the basis of sex under the Human Rights Act.