This has been expressed elsewhere, but I wanted to add an anaolgy to the Iax story.
Thought: much like Iax trapped part of the name of the moon in a box to partially bind her, for some reason Kvothe has trapped his own name (or part of it) inside his roah chest. This fundamentally altered him. We seem to get information in the frame from Bast and narration that Kote is not quite Kvothe, and some have already alluded to his potential loss of sympathy, naming, musical knack etc.
Perhaps whatever he did seemed so terrible to him, that he decided he was too dangerous and needed to bind himself. Or perhaps this was a way of hiding himself by giving up his true name. I'm note sure, but I think I lean towards the former of the two. In any event, him binding his true name could account for his loss of certain abilities, and his seeming like Kote at some times and Kvothe at others (akin to the phasing of the moon).
I think the culmination of the frame story will be the chest getting opened, and Kote returning to being Kvothe. Maybe he does something with that to fix what he did, or maybe it ends there. I don't have strong feelings about that either way.
To add to that, it is impled by Auri that names can sometimes be heavy. Kvothe's name must have gotten too heavy for him to wear, so he put as much as he could in his Thrice-Locked Chest. Bast remarks on the extraordinary weight of the chest when he tries to figure out how to open it. We also get a little foreshadowing for this when we recall Elodin's reaction when Kvothe tries to talk to him about Denna changing her name so often. This leads me to believe that Kvothe actually changed his name to better fit the innkeeper persona
Kote did sing a bunch of verses to Tinker Tanner at his inn in I believe the first book but it coud have been the second. It didn't say if he sung it well, but he was definitely singing in front of everyone and surprised them. So I don't know if he lost his voice but I don't know for sure.