Greeks were a mixture of more people,speaking same language,when Alexander Macedon was living.
When East Roman Empire took birth and adopted Greek as language,you can say for sure that Greek native speakers became a very various gathering of people.
I think they were calling themselves rather Romans,than Greeks.
However,some Turks conquered East Roman Empire and lots of population switched to Turkish.
The people that remained on the area that today belongs to Greece,or so were also quite mixed.
So what are you telling here ,that Alexander Macedon is of same ethnicity with today Greek speakers is just nonsense.
Alexander Macedon was not speaking today Greek language,he was speaking ancient Greek which is not exactly same language with today Greek.
What are you saying,that "Alexander Macedon was Greek" is as true as you would say that ancient Romans were same as today inhabitants of Italy or to say,Trajan was Italian or to say ,Augustus was Italian.
Now,go read more and stop preaching non-sense.
And to add one more thing,people of Macedonia have all the right to use that name,as North Germany is still called Prusia and Latvia and Lithuania are not saying Prusia is name that belongs to Balto-Slavic speakers,as Russians are still use the name Russia and Sweden are not telling Russia should stop using that name,because is linked to Rus,which is named of Swedes,how they were called some 1000 years ago and so on.