I think that this topic is so interesting. It has been my experience that most patients call me by my first name. However, I think that it would be more respectful to be called either Nurse (insert last name) or Ms (insert last name). The reason is that we refer to patients as Mr/Mrs. "Smith" , and we refer to physicians as Dr. "Jones", yet in nursing we are referred to as just our first name. Even worse than this is the situation where we introduce ourselves as " Hi, I'm [Mary, (for example)], Dr. Jones nurse (or Nurse Practitioner). This introduction implies ownership to the physician. It is such a sticky situation.
As nurses we want to build close relationships with our patients and have traditionally felt that the informality of first name basis, further enhances the nurse-patient relationship. But, does it really? In the NP role, I feel a little jilted to be called by my first name when the MA, receptionist, and other ancillary staff are called by their first name. I think that it should be acceptable to introduce yourself as Nurse "Smith", the nurse practitioner. Then once the relationship is formed, you can tell the patient that they can call you by your first name, if you wish. The same thing could be applied with physicians. You can introduce yourself as Nurse "Smith", the NP and then move on in a less formal basis if you wish. I have not, though, found many physicians that have me call them by their first name, so why should I let them call me by mine? (Just a thought!)