There are theories that the Romanians and Bulgarians are partly descended from the Thracians. It can't be really proven, though, as the Thracians just vanished from history at some point. Illyria is probably mentioned because Napoleon created the so-called "Illyrian province" out of parts of Croatia - Illyrianism was also the name of a Croatian movement for South Slavic unification - which the Serbs didn't like because for them it was Croatia trying to dominate the other South Slavs - ironically, the Serbs did the exact same thing themselves later on, in Yugoslavia. My uneducated guess would be that the foundation of the kingdom of Yugoslavia was when the whole trouble started, and after that it's a cycle of hatred. As I already said, I'm not from the Balkans, so I can only describe how it looks to me from the outside.
But back to topic: I liked DanubianCossack's idea a lot:
It's a fairly neutral name, without all the historical/emotional baggage the names Yugoslavia and Illyria have.