I am another who doesn't understand this. As far as I know, you have to provide identity documents when you do a DBS. So I had to provide my passport, driving licence atc, and disclose previous names.
Presumably this is to stop someone using a completely fictitious name.
If I didn't disclose a previous name, that would be an offence. I am not completely sure how it would be picked up if I had enough identity documents in my new name.
I can see that a transgender person has a lot more to consider than (say) a woman who changed their name on marriage, when putting a previous name on a form.
But the fundamental question is - are name changes picked up through any other means? If so, the check should clearly say:
We check previous changes of name. If you do not wish these former names to be given to your employer, please phone this helpline. This appears to be the reason given for trans people to phone it - so that all 'hits' are shown as Ms X, rather than some for Ms X and some for Mr Y.
But it doesn't say that, so it really begs the question whether there is another method to check? It beggars belief that they rely on individuals to provide all previous names with no other method of checking, but I am yet to be convinced otherwise.....