I believe even the ancient Greek historians referred to him as Alexander of Macedonia.
The Greeks then and now look at the Macedonians the way New York and California liberals look at the people of Indiana, Kentucky or Tennessee. Of course it galls them to think their civilization was conquered, and then spread, by someone they would consider a bumpkin by heritage.
And I claim some expertise in this perspective as a half-Macedonian Hoosier.
Actually, in Herodotus’ The Histories, there is a story about Alexander wishing to compete in the Olympic games (which were only open to Greeks.) In order to compete, Alexander had prove Greek ancestry. He was able to do so and was thereafter allowed to participate in the games.
His father was undoubtedly “Philip of Macedonia”; the Greeks contend it is a reference to THEIR Macedonia (a Greek province bordering the new country), not the new country created in 1991 from Yugoslavia. They feared the new country’s use of the name would later be used to contest borders.