In Back to the Future Part II, Marty's intense reaction to being called chicken is introduced. His mother Lorraine explains, "Your father's biggest problem, Marlene, is that he loses all self-control when someone calls him chicken," and this happens twice in the movie, once with Griff ("Nobody calls me chicken") and once with Needles ("Nobody calls me chicken, Needles, nobody!").
This trait also appears in Part III, just with the term slightly altered in order to fit the new time period. Now, Marty's response to Buford "Mad Dog" Tannen's taunts is "Nobody calls me yellow." The two agree to settle their differences in a duel on Monday, although Marty thinks that he and Doc Brown will have already gone back to the future by then.
Marty's ancestor Seamus tries to dissuade him from fighting Tannen: "You could have just walked away, and nobody would have thought the less of you for it. All it would have been was words, hot air from a buffoon. Instead, you let him rile you, rile you into playing his game, his way, by his rules." Seamus's wife Maggie comments that Marty (whom they know as "Clint Eastwood") reminds her of Seamus's brother Martin, and Seamus explains that "Martin used to let men provoke him into fighting. He was concerned that people would think him a coward if he refused; that's how he got a Bowie knife shoved through his belly in a saloon in Virginia City."
Later, Doc Brown gives Marty advice in a similar vein: "Marty, you can't go losing your judgement every time someone calls you a name. That's exactly what causes you to get into that accident in the future."
When the time for the confrontation comes, Marty is too busy trying to revive Doc (out cold from drinking a single shot of whiskey) to deal with Tannen, and when he looks at the photograph of Doc's tombstone that he brought back from 1955, he sees that it now has his own name (or rather his alias "Clint Eastwood") and tries to forfeit. Tannen renews his insults ("I think you ain't nothin' but a gutless yellow turd, and I'm givin' you to the count of ten to come out here and prove I'm wrong"), but this time Marty keeps his head and says to the crowd in the saloon, "I don't care what Tannen says, and I don't care what anybody else says, either." He maintains this mindset when he returns to 1985, and he doesn't race his new truck against Needles, thereby avoiding a crash with a Rolls-Royce.
The change in Marty's character seems to result from a combination of these factors (the knowledge of a dead relative with the same name and impulsive tendency, Doc's hint at a future accident, the tight time schedule available to Marty and Doc to meet the train they need to push the Delorean down the track so they can go back to the future, and the photograph of the tombstone that seems to foretell his death), but there may be an additional, more subtle cause.
Shortly after Marty first encounters Tannen, he's able to identify him because he overhears the bartender call him "Mr. Tannen." He remembers him from a video playing in Biff's museum in Part II and says, "You're 'Mad Dog' Tannen." To this, Tannen replies, "'Mad Dog.' I hate that name. I hate it, ya hear? Nobody calls me 'Mad Dog'!" and then proceeds to shoot up the floor in front of Marty. Tannen's response to being called "Mad Dog" ("Nobody calls me 'Mad Dog'" followed by a violent outburst) is basically the same as Marty's response to being called chicken ("Nobody calls me chicken" followed by a lack of good judgement). Marty may recognize that he shares this trait with someone he dislikes and consequently re-evaluate and change himself.
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It also occurred to me that McFly is an appropriate name in light of the movies' theme of family relationships, particularly between father and son, because the "Mc-" prefix comes from the Gaelic word mac, which means son.
