Sorry i know this post is about a month old but I've just signed up and wanted to say that they're only desperate to find the name and place of your employer so they can list that they found you the job and get their fat commission pay.
I've had the same from a branch of Job Prospects. I asked the case manager to provide evidence from the Job Active Deed that I was indeed required to supply pay slips. He has failed to do so, however they have the power to make false reports (and did so)- he reported that I failed to attend an appointment and didn't have a valid reason: I was working and he was bent out of shape because I told him I wasn't supplying my payslips unless he provided the evidence. During a phone call he made the unprofessional and inappropriate comment "when I first met you, I was in love with you"... As a result I have had intimidatory tactics such as condescending comments about my receiving welfare, humiliating treatment at an appointment-- I was made to have the appointment standing at the front reception counter in front of other jobseekers who were waiting and walking in.
Perhaps in future you might like to consider printing up you own attendance form and get them to sign it every time you go to the job search agents office. You might also like to consider taking a diary with you and making notes of the conversation with the people you speak to as the conversation progresses. These are called contemporaneous notes and they carry a lot of weight at any hearing. Make no mistake, they document the meeting with you from their perspective. If at all possible, take someone with you to use their mobile phone to take a photo of you at the providers place and ensure the photo incudes the time and date. hope this helps