I got that message too when transferring my main six from White 1 over. It doesn't tell you which Pokemon are affected by this, but I had a hunch it was my Krookodile, "Fukawa" (named the main 6 after Danganronpa characters!); so I quickly changed it to "Foukawa" by means of the Gen 5 Name Rater before trying again, and the warning disappeared.
So if you get that message when getting to that stage, and you're attached to at least one of your Pokémon (like with The Damned's Flygon example), try and change it if you caught it in Generation 5 first. You'd be out of luck if it was in Generation 3 or 4 unless you've still somehow got them stored on their original cartridge you caught it from and you're able to name check using Gen 6's name rater.
Still yeah, this is bizarre o_o*