While using the title "Student Doctor" would not be improper, I would point out that the patient tends to only hear the "doctor" portion of the title. Also, if you use this with nursing and other ancillary staff in the hospital, at least in my personal experience, you may incite bitterness and snide comments meant to belittle you or even "put you back in your place."
Even as an intern/graduate, I still hesitate to introduce myself as Dr. Tye, but of course, my authority (be it little or nothing) to write orders, admit patients, and make decisions, comes from the title. So I must use it. I still remind patients that Dr X will be by later to check on them, and clearly identify areas that I do not have the authority to dsicharge them or whatever. To nurses I introduce myself "one of the new interns" or "tonight's house officer." They can see your name badge title.
Giving yourself a title implies knowledge (hopefully we are increasing here) but mainly authority to answer their questions, and/or give definitive answers in areas we don't have the authority. As long as you are clear with your patients, you should be fine.
My recommendation is "Hello! My name is ______, I am a medical student working with DrX, who will be in shortly." Telling the patient which year you are also may just provoke more questioning, and you may find yourself just trying to get out of the room! Oh yeah, if you insert "osteopathic", you may have just opened up another can of worms! 😀
Hope this helps!
