Take a look in the situations vacant column of the paper and add up how many of the ads disclose the name of the employer. I reckon the ratio would be the same here as it is there.

//"we can't tell them who we are or people won't apply"

Well, companies that advertise directly will necessarily tell you who they are because otherwise noone would know where to send the CV.

Where a company goes through an agency, there are two reasons for not disclosing the name of the company, completely the opposite of your suggestion.

From the company's point of view, they may not have a human resources department or they may simply prefer to free up their own staff by paying someone else to do the gruntwork of vetting a wash of CVs. If people knew which company, a bunch would apply directly to the company, thereby defeating the purpose of paying the agency & cluttering up their mailbox with CVs they didn't want.

From the agency's point of view they prefer to keep their clients confidential partly to stop people from undercutting them by going directly to the company, and partly to avoid other agencies trying to nick their clients. When I was in the UK, a lot of competing agencies often tried to wheedle out of me the companies I'd already applied to.