Johan Kaufmann was a psychiatrist and the student of Professor Adam Wright. He was the companion of John Wakefield. He first appeared in Episode 3. Wakefield seems to be very fond of Kaufmann, as he mentions Kaufmann with every major discovery he has done from Episode 5 onwards. He even loses his entire motivation to look for Devitt when Kaufmann disappears from play. Kaufmann dies of an unknown disease at the end of episode 6.
It’s possible that Kaufmann was (or is) part of The Playwright. He certainly knows more than an uninvolved person should. At the start of episode 6, Wakefield is puzzled by the death of Miss Konhe. She seemed to exploded into a storm of crows. Somehow Kaufmann was aware that this might would happen and proposes to get help from his former mentor Wright.
It is possible the Playwright told Kaufmann to get close to Wakefield in order to find out what he knew. Of course, if it weren’t for Kaufmann, Wakefield wouldn’t know much of anything. Maybe Kaufmann was under orders to get Wakefield to do something, but I’m not sure that Wakefield would be very important to the Playwright. From their perspective, Wakefield’s main asset might be that Devitt trusts him. But would that matter to the Playwright? Maybe Kaufmann faked his own death. But why would he beg Wakefield to go to Éilís Mór and then fake his death? Kaufmann’s death was so upsetting to Wakefield that he almost didn’t go.
I’m guessing that Kaufmann was an independent investigator, just like he seemed to be. He probably worked with Wakefield because he needed a collaborator that he could trust. I’m sure Kaufmann didn’t tell Wakefield everything, but it’s hard to say whether he withheld any important information.