Extreme apologies for the title, I have tried to write this in the least controversial way possible, but I know this is a very politically divisive topic.
I work in a field adjacent to the history of northern Greece, and know many Greek scholars who feel very strongly that North Macedonia should not be called as such and that the name invalidates Thracian heritage. Having read about the agreement on the name of North Macedonia at the time, I was able to find a lot of reasons why many Greeks dislike this name and the usage of the Vergina sun on the North Macedonian flag, but no news outlet would explain the North Macedonian perspective.
So, what historic reasons are there for the North Macedonian association with the Macedonian name?
Its a very complicated issue, but ill do my best of explaining the North Macedonian side of the equation
The region of Macedonia has taken many shapes and sizes over history, however well be focusing on the Ottoman one (this comprises roughly of the region in Greece, all of North Macedonia and the Pirin region of Bulgaria). As the old Ottoman censuses and maps tell us, the region was mostly populated by mostly Macedonian Slavs, Macedonian Greeks, Macedono-Romanians (Vlachs), Turks and Jews. All of these people (except the Jews and Turks) espoused a Macedonian identity and shared the same heritage, religion and culture, the only dividing point between them being their language and political interests. The fruit salad Macedonia was named after this region after its diversity, yet sense of belonging together at the same time.
The greeks were very much the first people in Macedonia, however around the year 600 the first Slavic migrations took place in the Balkans. The Slavs that settled down in Macedonia found their new home in the Byzantine empire and lived side by side intermixing for centuries with the natives. Since the Slavs were so big in numbers though, this never led to them being assimilated, in fact the opposite happened, they assimilated a big chunk of the natives by this intermixing, while adopting their culture and traditions. This can be confirmed by genealogy in that the Macedonian Slavs have the most native DNA out of all the people in the South Slavic group
Before the Balkan wars and the treaty of Bucharest happened, the region of Macedonia was once again a warzone of the Balkan powers (Greece, Bulgaria, Serbia) all seeking to legitimize their claim on the territory which they did by church influence or opening schools for the children. In those very same schools, specifically the Greek ones, Greek teachers themselves taught the Slavic children that they were indeed the product of ethnic mixing and regardless of their language they were still the sons of Alexander just as much as their greek speaking compatriots.
Based on these three main points North Macedonia claims that ancient Macedonia and all that it encompasses should be shared instead of being regarded as the history of Greeks and no one else