What do the letters after a dermatologist name mean?

It depends on what letters you're talking about. If they are an M.D. or D.O. (equivalent degrees), that means he or she is a Medicinae Doctor (Medical Doctor) (Latin for "teacher of medicine") or Doctor of Osteopathic Medicine, the specific medical degree the physician possesses. A dentist will probably have DDS, "Doctor of Dental Surgery".

Many physicians are affiliated with some group of specialists or other and will list those after their name also; for example FACS stands for Fellow of the American College of Surgeons.