Why were Macedonia Syria and Egypt called Hellenistic?

Hellenistic means relating to Greek history, language, and culture from the death of Alexander the Great to the defeat of Cleopatra and Mark Antony by Octavian in 31 BCE. During this period Alexander the Great's Greek culture that he spread to the lands he conquered, flourished, spreading through the Mediterranean and into the Near East and Asia and centring on Alexandria in Egypt and Pergamum in modern day Turkey.