The Macedonians spoke their own native language which was unrecognizable by the Greeks. The very label barbarian literally means a person who does not speak Greek. Though Alexander spoke also Greek, loved Homer, and respected his tutor Aristotle, there is much evidence that he hated the Greeks of his day, just like his father Philip II. Philip had razed to the ground the Greek cities on Macedonian territory (including all 32 Greek cities in Chalcidice) and enslaved their inhabitants. Alexander the Great thoroughly destroyed Thebes. His Asian empire has not once been described as "Greek", but is correctly called Macedonian for he won it with an army of 35,000 Macedonians and only 7,600 Greeks, and similar numbers of Thracians and Illyrians who were all forced to fight with their Macedonian overlords. The overwhelming number of Greeks however, 50,000 in total (Curtius), had however, distinguished themselves on the side of the Persians and fought fiercely till the end against the Macedonians. For instance, at the battle of Granicus there were 20,000 Greeks, out of which the Macedonians killed 18,000 and the 2,000 survivors were sent in chains to Macedonia (Arrian, Curtius). Arrian specifically speaks of the "old racial rivalry" between Macedonians and Greeks that characterized this battle. At the battle of Issus, there were 30,000 Greeks on the side of the Persians to fight Alexander, and their survivors also fought at Gaugamela along with the Albanians and the Persians, against the Macedonians.
The question of the use of the ancient Macedonian language was raised by Alexander himself during the trial of Philotas, one of his generals accused of treason. This is what Alexander has said to Philotas:
"The Macedonians are about to pass judgement upon you; I wish to know weather you will use their native tongue in addressing them."
"Besides the Macedonians there are many present who, I think, will more easily understand what I shell say if I use the same language which you have employed."
Than said the king:
"Do you not see how Philotas loathes even the language of his fatherland? For he alone disdains to learn it. But let him by all means speak in whatever way he desires, provided that you remember that he holds out customs in as much abhorrence as our language"
by Peter Green
The Macedonians did not have Greek names. It is acutely judging by the distinctiveness of the surviving Macedonian names and glosses, that many scholars proved that the Macedonians were not Greek. Today, people of different ethnic backgrounds carry same names like Peter, David, Daniel, etc. These names are universal just like the names of Alexander and Philip were, and therefore, these names are not a proof that the Macedonians were Greek, since these names are found in other non-Greek nations.