Congrats!
The doctor would probably be a medical doctor (GP) or a psychiatrist, depending on the clinic. The second person is probably a therapist of some sort: most psychologists and counsellors do not have medical degrees so their titles will be the same as any other muggle.
And yeah, it's very annoying that the GICs correspond with us using our legal names until we show them evidence of an official name change. You'd think that they of all people could come up with some sort of accommodation. I have an appointment with someone relatively high up in NHS trans* services in a few weeks' time; I'll make sure I mention this.
If you've changed your name by Deed Poll, have you changed your name with your GP yet? There is a procedure that needs to be followed, but basically you start by telling your GP's Receptionist that you've changed your name and will need a new NHS number. They can't change your title or gender on their system because it isn't set up for trans* people (unfortunately); it's happy to change a woman's name on marriage but it doesn't expect patients to swap genders. (NHS numbers are gender-specific, so they need to issue a new number if we alter our gender marker).
So they'll get you to write to
your local NHS CCG telling them your birth name & date, your address, your GP's name & address and your NHS number (if you know it), enclosing a copy of your Deed Poll. They'll issue a new NHS number for you in your new name & send it to your GP for their records, at which stage it's a good idea to ring the GIC and give them your new details.
It'll also mean that your prescriptions will be made out using the correct name and title, and that you won't have to identify yourself as the wrong gender every time you visit your GP.
