Frank seems to go out of his way with a theatrical lynching, instead of say, putting a quick bullet to the man's brain. So for Frank, It's Personal and treachery was probably involved.
Some of the names that Harmonica gives to Frank were other deceased members of the gang who outlived their usefulness, as upon hearing them, Frank reacts with a surprised familiarity reserved to former comrades, not to regular or random foes. One of the names was actually the real name of Harmonica's brother.
Dave Jenkins, Calder Benson [...] Jim Cooper, Chuck Youngblood.