What’s in a name?

Generally they refer to each other by the gimmick name. So yes, Ryback would be referred to as Ryback. And people generally call HHH "Hunter". There's some exceptions where guys have had other names longer than their WWE tenure and people just refer to them by the old name as a habit (people called Mick Foley "Cactus" for years before his real name became the more well-known one, for example) but generally it's just the name you hear on TV.