We've discussed these issues before on this board. It's still unclear, I think, whether there is any mechanism that will flag a name change (for any reason) on a Disclosure certificate/check.
www.thetimes.co.uk/article/trans-status-of-recruits-must-be-disclosed-to-employers-dp9lfzqh6?shareToken=753baba1e8e25570303785a187b2d61d
'Susan Smith, from the campaign group For Women Scotland, said disclosure checks rely on the honesty of the applicant in revealing past names or identities. “In Scotland, however, the government’s determination to allow anyone to change their legal sex will add further complications, not least for employers who wish to invoke the genuine occupational requirement which allows them to reserve posts for members of one or other sex.”'