When do headhunters tell you which company they are recruiting for?

Enid's picture
Rank: Baboon | 120

Hi All,
A question to those who were headhunted or know someone who was. A headhunter contacted me about a job in a "tier 1 PE fund". I'm not really looking for a new job and till now I always turned down invitations from headhunters but this time I got curious.

When will I find out who they are recruiting for? I assume they would interview me first but when will they tell me the name of the company? During the interview? A few days later? Only if their client likes my resume?

Thanks for your help!