I'll be honest, the name "Hoss" is so ingrained in the character, I'd never even though about even if Hoss had a real first name. He was simply...Hoss. And it certainly hadn't occurred to me that if he did have a first name, that they'd ever use it on the show.
But in this particular scene, some older, respectable gentleman from San Francisco had come to the Ponderosa to meet his grown-up granddaughter, the child of his estranged son. And Ben Cartwright was introducing him to the fellow. And for whatever reason, after introducing Adam, he introduced his second song by his given name, and then added, "We call him 'Hoss.'" (The gentleman's other granddaughter, who accompanied him on the trip, then referred to him as "Horse." To which he replied, "No, man. It's just 'Hoss.'"
But the big deal wasn't that he was Hoss and not Horse but that he had a real name! You're free to take a guess here. I'll tell you below his picture, played of course by Dan Blocker..
For those who are keeping records of such things, you can now complete the "Hoss" line of your document of records.
Hoss Cartwright's first name is Eric.