Do Greek people really know that Alexander the Great is from Macedonia?

Answer 1

They most certainly did - they held the Macedonians to be very inferior, and knew Macedonians spoke a different language (when Alexander gave orders in Greek, their commanders had to translate them into Macedonian). Alexander's father Philip Ii had tried to counter this by faking descent from early Greek kings and running Greek cultural activities.

Answer 2

Greeks from Alexander's time were well aware that Macedonians had a different culture and different language. However, Greeks today consider Macedonia to be part of the wider Hellenic Community and see no true distinction between the Macedonian culture and the Greek culture. Moreover, the current country of Macedonia is primarily made of ethnic Slavs who migrated to the region from Eastern Europe long after Alexander's time. As a result, modern Greeks consider Alexander the great and other Macedonians as ethnically Greek, while still conceding that he is Macedonian.