Even the application of the name to North Macedonia is more a Roman thing than anything else. We don't call all of Greece (not to mention all the other lands conquered by Alexander) "Macedonia" just because it was conquered by Macedon back then ...
The current people living in modern turkey that were greek back centuries ago and had to assimilate due to various reasons from greeks to turks, would current greeks nor accept them as part of their culture and greek identity now? Would you say that current turks and greeks share some identity despite the annihilation of the byzantinians?
Would the aromanians of modern greece not be accepted as being part of the greek identity?
Would the bulgarians not identify with their mongol steppe nomad overlords that came over in early medieval age and started a khanate over the local slav populations?
Would the modern hungarians claim that they are in fact mongol asians?
These are complicated topics, and politics are just making it worse. There is no definite answer, because the truth lies in who has more power to enforce it. Both greeks and macedonians drown their daily life struggles and sorrows by beating the nationalism drum, so that the corrupt politicians can scream stupid lies on the microphones so they can continue with their corruption, and the common people eat it up like porridge. History is much more complicated.