Depending on the purpose of the e-mail, you could always consider skipping the name and just going with "good morning." I've noticed that when they write or respond to me, they usually just jump straight into the message, rather than starting with the greeting.
Obviously, if the note is just to ask for clarification of an assignment, this is okay, but, if you are asking for a letter of reference or something more important, you would want to stick with the formalities.
I still have problems with this, because although my professors are "Doctors," they are also lawyers, and most lawyers don't like being called "doctor." So I just go with "Professor." It seems the safe way, at least in my situation.