One of the reasons you are asked is to work out how important it is to see a doctor, urgent or routine.
If you are really ill and desperate to see a doc straight away then it helps if you can inform them of your symptoms. Your patient confidentiality applies to the receptionists as well as the doctor, after all, they type all your stuff up on the computer.
Unfortunately it is very rare that any conversation between you and the receptionist is very private if it is face to face as the whole waiting room can listen in.
I personally tend to have no problems, I give my name first then ask for an appointment, if anything, they want me there far more than I want to be there.