"A fine, fine man, alas, gone to his reward."
– Harry Mudd, speaking of the real Walsh, 2266 ("Mudd's Women")
Leo Francis Walsh was an alias used by Harcourt Fenton Mudd in 2266, who was then engaged in the business of providing wives for settlers on Ophiucus III.
According to Mudd, the real Leo Walsh was the man originally slated to captain his ship, but he "passed away, suddenly" before the trip. As he was taking the man's place, Mudd claimed he also took Walsh's name "in memoriam, as it were." (TOS: "Mudd's Women")
The real Walsh was only mentioned in dialogue.