Can you tell me a bit more about the company?
Typically you'll have a phone conversation with the recruiter when you first express interest or when they cold call you. Very, very often simply asking them for some more details about the company can get them to disclose the name. It's rare for companies to request their name to be withheld and it's usually the recruiters that avoid disclosing the name in initial contacts. But if they get the impression that you're asking in good faith and are genuinely interested in talking further then they'll often just tell you.
Even if they don't, if they give sufficient detail (headquartered in City X, employee count of Y in the US, active in sector Z, ...) you can often put the pieces together. But that typically requires that the company is fairly large and searchable or that you're in a relatively small industry.