The Hellenistic era was launched by Alexander the Great, and his death is usually defined as the starting point. The Greek word Hellenes (Ἕλληνες) was in use before, during, and after the Hellenistic era as far as I can tell. I wonder whether Alexander's conquests and the onset of the Hellenistic era had an effect on the meaning of the Greek word itself. Was there a change in meaning from the time before Alexander to the time after him in the meaning of Ἕλληνες or related words?
With the spred of Alexsander's empire, a quasi-Greek culture spread throughout the countries he conquered. It rapidly became the prestige culture for those that wished to be up-to-date and cosmopolitan. Since these people were not Greekand the culture was not pure Greek, the people were known as Hellistists or Greek-like and the culture was known as Hellenistic.