This was another of the questions from my Swarthmore math talk, which I'm revisiting and answering on the blog.
To varying degrees, all of the props at the casinos in Los Angeles try to blend in with the customers. Some will outright lie to customers about whether they are props, while others might make it obvious without even being asked. In general, none of the props wear any identification, and the casinos operate under the assumption that it's better if customers don't know that there are any props at all. I think we were technically supposed to tell people the truth if we were asked, and I know that the floorpeople needed to inform customers of who the props were if asked. Beyond that, there was a lot of secrecy. Shortly after I started at the Bike, we had a meeting in which one of the supervisors told us that if someone asks us if someone else is a prop, we should just say we don't know. "It's not really lying because for all you know, he quit that morning and isn't a prop anymore." If you are concerned about who the props are, just go ask a floorman.
In practice, the regular players at a casino do know who the props are, but new players usually do not. In fact, the new players usually don't even know that there are any props at all. I didn't know when I started going to casinos.