The senior surgeon of a brigade or division frequently was mentioned as chief medical officer. However, there was no official designation beyond the two ranks mentioned. The staff of most regiments included a surgeon and an assistant surgeon. Artillery batteries usually had an assistant surgeon on staff. Assignments were usually made by the Medical Director's office in Richmond. For that reason it's sometimes difficult to know who was serving with a regiment at a given period of time.
Medical officers had to be reviewed by a medical board. Some refused to stand examination and were not commissioned.
As for all commissioned officers, there was a date of appointment, date of acceptance and date of rank. Officers received pay based on date of rank.