Here are a list of the appearances made by Glenn Strange on 'The Rifleman':
"Duel of Honor" - Cole, stagecoach driver
"The Deadeye Kid" - Shotgun Guard
"The Woman" - Joey, Stagecoach Driver
"The Blowout" - Stagecoach Driver
"The Spiked Rifle" - Zack, Stagecoach Driver
"Miss Bertie" - as - Guess what! - the Stage Driver
Since he was the stagecoach driver or shotgun guard on the coach in each of those six appearances, it's O'Bvious that Glenn Strange was playing the same guy in each of them. There must not have been a very observant continuity girl using the show's bible, however, since three times out of those six, he was given a different name each time. (In the other three, he was just the stagecoach driver.)
I think the easiest splainin would that his first name was Joseph, his middle name was Cole, and there were some in North Fork, New Mexico, who knew him as "Zack" for some reason. Despite his gruff appearance, he was probably an easy-going guy and would answer to either name if you called him - just so long as you didn't call him late for supper at Madera House. (Ba da dum!)
I could have said that his last name was Cole, and that he answered either to his first name, his last name, or that nickname. But I think it's a pretty safe bet that his full name was Joseph Cole Noonan. I think Joe Cole, AKA Zack, was the brother of Sam Noonan, the bartender at the Long Branch saloon in Dodge City, as seen for many years on 'Gunsmoke'.
Since we never saw them visit each other on their respective shows (Gee, I wonder why....), it could be that they had a falling out. Perhaps Joe was using his middle name of Cole as his new last name instead of Noonan to declare the split between them.