On the one hand, the Greek position is that ancient Macedon roughly corresponds to the territory of the Greek region of Macedonia.
The Macedonian historical narrative has not been constant in treating the history of the ancient Macedon. In socialist Yugoslavia the official narrative elaborated how the Macedonians are a nation inhabiting the geographical territory of Macedonia, since 600-700 AD when Slavs first settled in the Balkans (Tashkovski 1976, Apostolski 1979).
Greece would be 'left' with the name 'Macedonia', to invoke ancient Macedon. 'Makedonijans' could co-exist along 'Greek Macedonians.' As part of the compromise a declaration in which the 'Republic of Makedonija' would acknowledge that ancient Macedonia is part of Greece's historical legacy could be adopted by the government in Skopje.
This element of the dispute pertains to the 'right' to project the ancient Macedon history as being integral part of the ethno-genesis of the Greek and/or the Macedonian nation.