I'm also an Advanced practice Nurse Practitioner who xan prescribe, with a PHD, so could go by Dr. TheVirgin, and do in my non-work life.
However at work (Hospital, not GP) I introduce myself as 'Jane TheVirgin, the Nurse Practitioner caring for you today'. My photo ID is clearly visible and says Nurse Practitioner though I do have a sticker over my surname.
I do think it's misleading. But I'm also not sure what the answer is, because they are legally entitled to use their title and knowing some of the attitudes, wouldn't agree not to.
Maybe if they are a PHD, we change it so they have to have their ID visible, which it should be anyway, and they must introduce themselves as 'Dr. Smith, the Physicians Associate'. Though I do also see if someone isn't clear on the new positions they'd still assume qualified medical Dr, GP and just not know what a Physicians Associate is.
I really don't understand WANTING to be mistaken for a medical doctor in a hospital. I got my PHD for knowledge, I do not want to be as responsible as a medical doctor at all.