Alexander the Great and his father, Philip II, were Macedonian. So why is he considered Greek when it comes to all the stuff he conquered?
Because back then, Macedonia was in the Hellenic (so Greek) cultural area. Over the course of the last 2000 years, it shifted to become a Slavic region when the Bulgars invaded. It's actually a tough debate since the modern republic of Makedon has little to do with the Macedonia kingdom of the Antiquity. But modern day Greece also has little to do (genetically and culturally) with the Hellenic kingdoms and republics of back then.