Another thought
Seeing this again tonight (wanted to see the whole thing completely and with more focus), I would like an answer to this: When Kermit is thrown into the Russian prison because they think he is Constantine, at first they are calling him Constantine but eventually even Nadya calls him Kermit. Why? If they believe he is Kermit, wouldn't they then release him? In fact, Nadya even shows Kermit the Muppets on tour and says something to him about it, so she has to believe Kermit is telling the truth.
If the idea is that they think, "Okay, he wants to be called Kermit, fine, we'll call him that," then have a line that says that.