I couldn't even guess who most of these characters are.
Without referencing Memory Alpha, the ones I can identify (skipping the bolded ones, since we all know them)
M'Benga: Operated on Spock when he was injured in TOS A Private Little War
Selar: Accompanied the away team to Graves World and looked after Ira Graves in TNG The Schizoid Man. Also mentioned in multiple TNG episodes
Dalen Quaice: A friend of Beverly Crusher's, TNG Remember Me.
Miranda Jones: Travelling with the Medusan Ambassador, TOS Is There in Truth No Beauty
Jeremy Lucas: A friend and writing correspondent of Phlox. First mentioned in Enterprise Dear Doctor, not seen until Cold Station 12
Martin: Another Enterprise D doctor, took over sickbay when Crusher was incapacitated in TNG Violations.
Elizabeth Lense: A medical school rival of Dr. Bashir's, visited the station at some point in DS9 season 3, can't remember the episode.
Christine Chapel: Well, we all know who she is.
Sarah April: First CMO of the Enterprise, Robert April's wife, seen in TAS The Counter-Clockwise Incident.
Nambue: CMO of the Shenzhou, Discovery The Vulcan Hello.
Elizabeth Dehner: Psychologist on the Enterprise, became infected with the same abilities as Gary Mitchell, TOS Where No Man Has Gone Before.
Helen Noel: Another psychologist, had a relationship with Kirk, TOS Dagger of the Mind.
Toby Russell: Medical specialist brought in to operate on Worf's spine, TNG Ethics.