Who he is
Cole Cassidy (formerly Jesse Mcree) is a character in Activision Blizzard's video game Overwatch. I believe he was one of the original characters (not an addition to the roster), and is considered a damage or "dps" character (as opposed to tank or healer/support.) He's a cowboy; he wears the hat, he's got the six-shooter gun, all that (even though the game's set in the far future? Cowboys make a comeback somehow, with hoverbikes. But Overwatch's lore is about as good as Marvel's so... whatever.) He's got a robot arm because cyborg cowboys are cool, I guess.
Lore
Cassidy was a member of the Deadlock Gang, a group of criminal cowboy-fellows that performed heists. I believe he was in a romantic relationship with Ashe, who led the Deadlock Gang (or perhaps he led it and she picked up after he left, the lore isn't too clear.) Overwatch offered to wipe his slate if he joined them, and he left his life of crime behind to become an Overwatch agent.
When Overwatch was formed, a secret-service branch of Overwatch was also formed, known as Blackwatch. Strike Commander Jack Morrison/Soldier 76 headed up Overwatch and directed all their missions, while Gabriel Reyes/Reaper directed Blackwatch. Cassidy was one of the members of Blackwatch, and participated in all the undercover missions that were too dirty or illegal for Overwatch. He also was one of the few people that knew about Echo.
After Overwatch disbanded, he became a traveling mercenary, aimlessly wandering the southwest in search of meaning.
Controversy
The controversy: throughout all this and since the game's conception, his canon name was "Jesse Mcree". He wasn't known as Cole Cassidy, or to be Cole Cassidy. Blizzard named the character after a real life Jesse Mcree, who was the lead level-designer for World of Warcraft. Jesse Mcree was laid off this year over sexual assault allegations, and they changed the name of the character to Cole Cassidy. The canon explanation, though, is that Cassidy was his real name and Jesse Mcree was an alias that he used. So, in-game and in all the media on the website, he is now known as "Cassidy". It's controversial, but most people I've spoken to in the in-game chat think that it's stupid. Many people even refuse to call him Cassidy, and still call him Mcree after corrected.
Personally, I don't think it matters. If they want to change it, fine. If they didn't, it wouldn't have mattered. I somewhat doubt that anyone's going to say to themselves "I'm not going to play this game because they didn't change the name of a character." A lot of people already think Blizzard is evil (they apparently have a lot of sexual assault allegations), but it really doesn't change anything.
Abilities
Cassidy's main weapon is a six-shot revolver. It's precise, if you have your crosshair directly on a far-away target you'll hit the target (I know because I've gotten picked in the past that way, some people are just too good). You can either shoot one at a time, or let off all six shots quickly with much less precision (but have a longer reload as a consequence).
His special weapon is a little grenade he can throw that explodes on impact with a character or the ground, and stuns enemies for a second or so. (Just enough time for you to use his six-shot point-blank and get a kill).
Another special ability he has is to dodge by rolling; he lunges in the direction he's moving and rolls.
His ultimate ability, called "deadeye", will shoot all enemies within his line of sight for a lot of damage, usually killing everyone. While he's doing it, though, he's motionless, so if you know where he is you might be able to get a kill.