The name "Chris Adams" appears in the introduction of that character in the script, but was never spoken or alluded to elsewhere in either the script or the movie. I have a copy of Screen Stories magazine from 1960 which also uses his last name.
In the script, Chris is described wearing a dark suit of good cloth, cut well, but threadbare. "In his late thirties, he has been around and, in the course, has developed a considerable manner best described as panache".
This fits Brynner much, much better than Sturges' original choice to cast Spencer Tracy in the role. Sturges had worked with Tracy before, but around this time, he was playing in "Inherit the Wind" and was well past his prime as a rakish gunsilnger. He did, however, more closely resemble his Japanese inspiration.
Also in the TV series, Vin has the last name "Tanner" which is not in the movie script.
We deal in lead, friend.
I don't remember where I heard it but, it was either in the first M7 or maybe the M7 Returns that Chris is referred to as a Cajun.