The name "Gilhooley" appears in ONLY ONE John Wayne movie: "McLintock!" (1963).
The character "George Gilhooley" is a pompous, arrogant, and ultimately comical antagonist in the movie, played by Patrick Wayne, John Wayne's real-life son.
The name "Gilhooley" has become a bit of a meme among fans, but its association with John Wayne is limited to this single movie. It's possible that the name's humor and the popularity of the movie led to its spread among fans, creating the impression that it appears in more films.