I've seen a lot of people referring to Alexander as Greek, even when his kingdom was known as Macedonian. What's the reason of this mixture?
I've previously answered this question in detail here, and expanded on it further here. In short, Alexander and his ancestors were indeed sometimes considered Greek, because Greekness was not an objective and measurable fact, but a socio-political status that Greeks could use as a tool to include or exclude. The Greekness of many individuals and groups was contested. The Macedonian royal house claimed Greekness, especially when it was politically expedient, and while some Greeks were willing to grant their claim, others rejected it. Their view on the matter largely depended on their political stance towards Macedon.
Culturally, Ancient Macedon was Greek-adjacent and elite culture was certainly affected by many Greek influences, but even the ruling class also maintained its own distinct customs and practices. No one really seems to have thought the general population of Macedon was Greek, and they may have spoken a non-Greek language - there is precious little evidence on their lives.
Well, he certainly spoke (a form of) Greek and, in European nationalism, language is often the defining boundary marker. The Greeks are those who speak Greek. Second of all, whatever we can call the “Greek world” in antiquity (there was obviously no state claiming to represent all the Greeks until the 1820’s), Macedonia was part of it... or at least thought of itself as part of it . Alexander was famously tutored by Aristotle as a young man. Aristotle was also originally from Macedonia, but he is generally thought of as “Greek” (Aristotle also left his hometown and went to study at Plato’s Academy in Athens when he was 17 or 18). Another thing to factor in is that by the time Alexander is aware, his father had conquered most of mainland and insular Greece (but not all of it, nor the part of the Greek world in Asia Minor under Persian rule).
But nationality was also different in those days. This can be seen in Alexander’s own behavior: he spread Greek culture (some of the states that emerged in his wake, like the Ptolemaic Egypt, continued to use Greek as a court language for hundreds of years) but he was also perfectly willing to take on the trappings of conquered cultures (particularly the Persians). Adopting Persian symbols didn’t meant giving up his Hreekness. We tend to think of national identity as one thing today: you either are Greek or you are Macedonian, you are Azeri or you are Kurdish, you are French or you are German. However, historically, in pre-nationalist times, it was much easier to invoke different identities in different circumstances, as these boundaries weren’t nearly so clear. Additionally, how identities “stacked” and “nested” and overlapped was more important. Was Socrates not simultaneously a Greek and an Athenian? Why would Alexander being Macedonian prevent him from being Greek? Were the Ptomelies in Egypt and the Seleucids in Persia simultaneous Greek and Egyptian/Persian? However you want to think of it, it just doesn’t really work to imagine our exact categories backwards in time because they weren’t the exact same as the categories that were socially relevant at that time.
I go into more detail, discussing Shah Ismail and Charlemagne, in these two posts here which I think will help add some more clarity: