I agree with the comments about procreation or not - Upton's marriage is private - but Upton explicitly said he wouldn't recognise a woman's right to say no to a male-bodied doctor treating her if he self-IDs into the female category, so where he works therefore is a matter of extreme importance for very many women in Scotland who cannot (for whatever reason, trauma, religion, other) cope with a male doctor.
If he doesn't want people discussing where he's practising medicine then he needs to recognise that other people - particularly his patients - are fully human too and their perceptions and feelings about their care matter as much as his (entirely fictional) belief he's a woman. It's a shame the regulator isn't enforcing informed consent, but given the very many horror stories about the NHS and the behaviour of senior managers in this and other cases it appears ideological authoritarianism is the main aim of the NHS these days, with patient care a very secondary concern.
IIRC there was something about a dementia patient being 'transphobic' because she only had the mental capacity to recognise reality and couldn't lie about it? In that context I think it's fair enough to want to know where he's working so he can be avoided.