I've always assumed it was pronounced with a soft c, like mass-a-don. But here recently I've heard it pronounced with a hard c like mack, Total War and Dan Carlin.
Also, would Alexander have called his empire Greece or Macedon or something else entirely? Obviously he'd still use regional names but what would you call the whole thing?
Disclaimer: I'm not familiar with the Greek spoken by the Macedonians, but might be able to explain the difference in modern pronunciation.
The Greek word for Macedonia was Μακεδονια (plus or minus some accents). The κ is a hard C in Greek, so would be said Mak-e-donia. When being translated into Latin a the Greek κ become the latin C, and as the English often use soft Cs we began to say Mass-e-donia.
A lot of academics and historians choose to use the pronunciation from the period when discussing a historical society, hence Mak-e-donia being used in some contexts. Latin readers are beginning to use the classical latin pronunciation, for example Cicero is said Kikero, rather than siss-er-o.
Unfortunately I can't help with the second part of your question- but I hope someone can!
This is an interesting question and a difficult one. The "Greeks" as we call them, did not refer to the Macedonians as Greek. They were Macedonians. They were considered to be barbaric, likely because of the differences between the Greek city-states and Macedonia. One notable difference was the adoption of the city-state system. Obviously, the Greeks on the Hellenic mainland operated as different city-states rather than as a region. Macedonia governed regionally, and this region included the cities of Thessalonike and Pella. This was a contributing factor to the division that Greeks and Macedonians experienced. Also, Macedonia spent centuries fighting barbarians in the North, thus missing out on many wars fought in Greece.
Another contributing factor was the style of military that the mainland Greeks used and the Macedonians. The Greeks focused on hoplite warfare. their armies would be largely composed of hoplites with helot skirmishers. The cavalry used by Greek armies were usually in a scouting or disrupting role. Macedonia, however, used cavalry to a much greater extent. The main reason for this was the geography of Macedonia. There was a lot of room for pastures in Macedonia, thus more horses could be reared and used in the military.
To get to your question, I doubt Alexander would have referred to himself as Greek. The cultural rivalry between Macedonia and Greek city-states was strong and one that I do not believe would have been erased in such a short amount of time. You mentioned Total War, Sid Meier's Civilization has always had Alexander leading Greece, until Civilization VI. Now, he leads Macedon, as he should. Alexander's empire can barely be considered Hellenic, which differs from Greek. Hellenism is the concept of cultural diffusion implored by Alexander. If anything, he would have referred to his empire as simply the world, for that was his vision. His goal was not to conquer the world, but to unite the world under one flag to end all wars. Ambitious and naive, but this is claimed by Arrian.