The main reason that the agency recruiter won't share the name of the firm is to "protect the client".  Another reason is so that you don't rush to the companies website and apply online before they can get your resume over to the HR department. 

If you have a good relationship with an agency recruiter, they should share the name of the firm unless they are doing a confidential search (replacing someone) for that company. 

Agreed that it is a two way street - you have to trust them, and they have to trust you.   

Your best bet is to find a recruiter that someone you know has had success with and work with that recruiter.  Once you have a one on one relationship with that recruiter and he/she knows that you won't go around them to a job, they will share all the details with you.  That is the relationship you want to have with your recruiter. 

As a recruiter, this subject makes me crazy.  I don't worry about something that could happen 1% of the time, such as a candidate going around my back to apply directly to my client.  I WISH all recruiters would be forthright about who they are sending the resumes to.  It would save everyone a lot of time and energy by not duplicating everyone's efforts.  On the same subject, I will not disclose my client if a candidate is not willing to send me a resume first because that means they are just tire kicking or being nosy.  I let all my contacts know that I do not send anyone's resume to a client without their permission first.  I just hate the impression of playing games with people and treat my candidates with respect and as a professional.

SMPS - I would agree with most of the comments on here.  I have been recruiting for 11 years, I'm a straight shooter.  When I qualify a candidate I can size them up pretty quickly in regards to their level of interest in the opportunity that I present to them.  I  know when they are just fishin' to see who it is that is looking and I know when they are serious.  When I sense they are fishin' I throw them back in the water without releasing my client's name.  When I sense they are serious I share with them my client's name.  It is pretty cut and dry, BUT, I do have a quick story for you which should make us all aware of what can happen.  Last week I qualified a candidate for a Director of Marketing position, and she was very interested and really excited about the position.  It was just up her alley and it was five miles from her home.  I told her who the company was, I emailed her my contact information and she in turn sent me her resume.  In between the time I was able to review her resume and correspond to my client her qualifications she took it upon herself to make some calls to some people she knew, one thing led to another and she submitted directly to my client before I was able to.  SOOOOO very annoying. I had to read her the riot act (calmly and professionaly of course).  Luckily my client and I have a solid and respectful relationship where I was able to explain what happened, and the candidate reitereated what had happened as well.  It's all good now, if they hire her I will of course get credit, BUT there are candidates out there like that that will pull that same silly stunt because they just don't know better or they don't really understand how it is we make our living.  That being said, this happens VERY rarely and does not deter me from releasing my client's name to the right candidate.