There was no movie titled "The Man With No Name", actually... There is what is generally considered "The Man With No Name Trilogy", however, based on the fact that Clint Eastwood played a character with the same mannerisms and the same costume in all three "Spaghetti Westerns" directed by Sergio Leone. The three movies were:

A Fistful of Dollars
For a Few Dollars More
The Good, the Bad, and the Ugly

Now, technically, Clint's character was *not* the same man in all three movies according to an Italian court, which heard arguments after Leone teamed with new producers on "For a Few Dollars More" and the producers of the original sued for ownership of the character.

Perhaps because of this, he is called by a different name in all three movies. However, the studio releasing the films in the US marketed Eastwood as "the Man with No Name!", possibly because his name was only said once in passing in the first flick. Or maybe just because it sounded cool.

I could give all three names here, but that's only because I looked this up after wracking my brain to figure out which Eastwood flick was called "The Man with No Name" and coming up blank. So I'll leave the rest of the board to provide an answer.