Short version: When PCs concede, the opponent should get "what they wanted from you", though the details should be negotiated with the PCs. However, the concession should not amount to being taken out.
The Fate Core book limits what concession can and should not mean. All from "Conceding the Conflict" (Fate Core 167):
Concession gives the other person what they wanted from you,
As the demon wanted the party to name him, it would seem reasonable for them to do so as they concede. As @Radhil suggests in his comment, how exactly the PCs do this should be agreed collaboratively.
you get to avoid the worst parts of your fate. Yes, you
lost, and the narration has to reflect that. But you can’t use this privilege
to undermine the opponent’s victory, either
That can make the difference between, say, being mistakenly left for dead
and ending up in the enemy’s clutches, in shackles, without any of your
stuff—the sort of thing that can happen if you’re taken out instead.
Taking this into account, it depends just how bad things are for the PCs if they name the demon:
- If it complicates their lives and the story in an interesting way, then that would seem like an excellent thing, in line with the whole spirit of the Fate rules.
- If it would limit their actions to the same extent as being shackled and under his total control of the demon, then that would be inappropriate for a concede.
Players in Fate have much more ability to change what actually happens in the story than in other games I've played. This means you could also revise the exact effects of the demon being named, if the naming happened as part of a concession.