Doc explains to Dr. Sam that he was named after Dr. Claudius Galen, who lived 129 CE - c. 216 in the area now parts of Turkey and Greece.
Milburn Stone was allowed to choose the first name for his character and chose Galen in honor of the physician.
Vera Miles (Dr. Sam) and Ken Curtis (Festus) also starred with John Wayne in 1956's The Searchers.