Hellenization

Hellenization (or Hellenisation) is the historical spread of ancient Greek culture or Hellenistic civilization, and, to a lesser extent, language, over foreign peoples conquered by Greece or in its sphere of influence, particularly during the Hellenistic period following the campaigns of Alexander the Great of Macedon. The result of Hellenization was that elements of Greek origin combined in various forms and degrees with local elements. In modern times, Hellenization has been associated with the adoption of modern Greek culture and the ethnic and cultural homogenization of Greece.

Read more about Hellenization:  Modern Usage, Modern Scholarship