This article is from the ER FAQ, by Rose Cooper email@example.com with numerous contributions by others.
The explanation given is that patients are made to feel more
at ease if they believe they`re being examined by a real doctor.
[This makes it all the more interesting that in season five, Carter
refers to his own medical student as "Miss Knight" in front of patients.
Hmmm...] Some people have reported that this is semi-common, or at least
acceptable, practice at some hospitals; others have claimed that this
is totally unethical.
Students are given nametags that have their names on it, but
not "Dr." or "M.D.". They`re taught not to be forward with the fact
that they`re only students, but not to be evasive about it either.
At the end of the second season, Carter graduated from med
school and received his medical degree, so he`s officially a doctor