My only issue with that was when a hospital receptionist asked my name, followed by my dob, and refused to let me write it down or take it from the form I had just given her. There was a queue of strangers behind me and I think that breached the DPA.
The DPA specifies they are allowed to use your information reasonably. Generally speaking, using your name to identify you is reasonable.
The DPA also doesnt cover you when giving your own information out, it strictly relates to how an organisation records, stores and uses your data. If you don't want to give out certain details that's fine, but you should expect some places to refuse you service if they can't reliably identify you.
However, in your example the hospital receptionist was wrong. They shoukd gave allowed you to write the information down, thus is what i instruct staff to do at the hospital where i work.
The DPA would be breached if they read your details off the computer to you to get you to confirm, particularly if you are in a busy waiting area. Basically, you giving your derails freely indicates consent. When they give out your details to you they have no way of knowing it is definitely you - an imposter could say yes to every question.
My main GP surgery still uses a tannoy, but the branch surgery just calls you. At both I am on such good terms with the doctors they just use my first name.
A hospital i go to (not where I work) uses screens. They put them in the waiting room and the cafe next door so people could go and wait in there if they wanted. It was supposed to be better than shouting.
The problem is, its an eye department and many of the patients are severely vusually impaired. They couldnt see the screens, so they had to turn the sound up on them so they said the name too. But most of the patients are elderley and many are deaf too, so the poor staff are wandering about shouting too!