I think this whole name dispute actually has very shaky base.
People of today's Macedonia by blood are same people as those who lived there thousands of years ago.
They did not disappear. Therefore, I believe they have claim to heritage of ancestors who lived there before.
Genetically, Greeks, Serbs, Macedonians and Bulgarians are all similar, since they are descended from Paleo-Balkan tribes (Greeks, Illyrians, Macedonians and Thracians), who were all related and native to reigon.
Fact that they speak Slavic language is because of Slavic conquering in 6th century (invited by Byzantium to fight Avars, according to Slavic migration theory), but that does not mean they magically changed into Slavs like those in Poland, Belarus, Ukraine or Slovakia, their blood and ancient heritage still remained with them.