I think it can be assumed that you can't just change your name and hide previous convictions.
As said up thread, if the intent of the "sensitive route" is not to out someone with a GRC (or new identity based on a driving licence name) it would be in some instances, say where a prison sentence was served, or a type of crime, would be an identifier of born sex.
It would be great to hear from someone who had actually had to do a DBS check under the conditions of the "sensitve route". It maybe that in terms of what the employer is told, nothing of relevance would be ommitted and the outcome no different.
It isn't for me about someone trying to conceal they are trans, for employers and service users that a whole other issue which many have not worked out how to deal with.
For me it is an issue of fairness, does the very kind, considerate, "sensitve route" mean that people who are trans are treated / judged differently at the expense of the DBS being as truthful and accurate as one where this option is not used.