Maybe I worked in retail too long, but I definitely sympathize more so with the manager than the customer here. The customer came across as whiny and clueless on how if a rule or policy is put in place, it has to be followed, and then acts all snarky even when he gets his way. The manager didn't handle it very well, but if the YT comment is true, it sucks that once again, an asshole customer gets their way, even if they were in the wrong, and the retail employee loses their job over it.
I've also had arguments with customers over the whole last name thing. In retail, regardless of how nice you treat customers, they're still going to hold you responsible if they don't get their way (even if you're just following policies set in place at a higher level), and it always comes down to 'give me your name and your manager's name' or 'I'll never shop here again.' I always refused to give out my last name, and instead would give my department, which would make the customers angrier, since once again they weren't getting their way. Luckily my managers would back me up though. There's no reason the customer needs to know that, especially given how easy it is to find people online.