For information, did your dialogue just close off after playing the flute correctly? It should usually just switch to the mephit right away, you don't need to click on him to interact with him, the dialogue just switches to him, as if he was part of the conversation from the start.
If it is dialogue related, it reminds of the issue I am having in the Underdark with a character there:
I can't progress with Nere's conversation for him to leave the Absolute. I saw it is working and not bugged, at least from previous patches on youtube, but my dialogue just loops back untill I exhaust every option I have that would lead to that outcome. I have made a post here if anyone would like to see the images for the problem, as explaining by words might not render the picture, I hope it does though! Doing my best here!
I believe it might be the same issue you are having. as that dialogue too would close if it wasn't for the non-check option, as that is the only one with a different outcome, and the other options just disappear after being done to an extent, and the mephit's dialogue would lead to him always asking you for his name, so maybe it is not triggering, as in my case, locking you out from telling him his name. There ARE wrong options there, but he has to have a scene where he asks for the name before you can answer, I believe that is what is not getting triggered, much like my case, where the dialogue doesn't trigger, not progressing (and in my case there was no choices afterwards, just one line and end of dialogue, yours lead to something, in this case a list of name-options).
If that is the case, I would believe it must have been broken with either this month's patch or the one before, as videos I have seen on youtube had the dialogue with the NPC from my issue working from 2 months ago. If you can, I would try and load a less recent patch to see if that gets it to work again, but otherwise would wait and see if it will get fixed in the next patch (there have been issues with cutscenes as well, could be related? I remember seeing the mephit and doing the scene and quest though, but I am thinking it might have been before this month's patch, so I might try from that just to be safe).
