A lot of recruiters won't list the company that they are recruiting for. I assume this is because you could just apply to the company directly and they wouldn'

A lot of recruiters won't list the company that they are recruiting for. I assume this is because you could just apply to the company directly and they wouldn't get their fee. One time I asked the company who they were recruiting for. They told me the company name and I replied with "I already work there." This was on LinkedIn where my current employer is on my page and anyone can see it.