If they tell you the company, what's stopping you from turning them down and going directly to the company? I'm pretty sure that's the main reason they don't tell you the company.
I've had recruiters tell me right upfront which company they are dealing with.
Unless, of course, I hate dealing with them. In which case I'm not going to get hired through them in the first place.
Why would I do that?
HINT, you want the exclusive recruiter..