If I was at a startup and looking to move to a new one, I wouldn't want it to be public knowledge that I was looking until I at least talked with a couple companies.
That being said, I'm assuming you'll be told what company is interested in you (if any) when/if they make contact rather than the usual recruiter nonsense ie. "A company in the financial services space" etc etc
This way, you keep your site single-blind (to keep people from skipping using your service) and if a company happened to be in the list, the person could still use your service (just hiding his/her info from that party).