Galen was an inspirational medical practitioner whose name was among several Starfleet doctors, their patients, and medical personnel in historical and literary contexts, which were included in the Emergency Medical Hologram programming.

When Kes suggested that The Doctor could name himself after someone who inspired him, he mentioned Dr. Galen, Dr. Salk and Dr. Spock. None of those names, however, were ones The Doctor could see himself with. (VOY: "Ex Post Facto")

This character was only mentioned in dialogue.
"Galen" is likely a reference to the famous ancient Greek physician of the same name.
According to the Star Trek Encyclopedia (4th ed., vol. 1, p. 293), Galen "postulated that Human arteries carried blood, not air as had been previously thought."