Yes, that's a ridiculous reason for his name, especially as the Corinthian had his name at least before Dreams imprisonment, and possible a couple of centuries before that (I can't recall if he's refered to by name as far back as that, but he does accompany Dream during the 18th(?) century). A Corinthian is just a name given to someone prone to luxury, a bon vivant as it were.
I've written the Corinthian in fanfic (a Batman and Robin one I must finish some year or other) and he's a character I find incredibly uncomfortable to write. I CAN write him, but I want to scrub my skin raw with carbolic soap afterwards because he's just so... fucking creepily grotesque.