Hellenes
According to Thucydides, Hellenes were called the people of Hellas. Greek mythology states that were named after Hellene. A more scientific approach places the origin of the name in Epirus, the land of the Dorians, where people were called Selle or Helle. The spread of the worship of Zeus in the rest of Greece (the basis of which was in Dodoni), the Dorian tendency to form amfictionies and the increasing popularity of the Delphic religion lead to the use of the name in a way that denoted the people that today is known as Greeks (name originated from another Epirus tribe, the Graecoi). Before that the Hellenes (or Greeks) were distinguished in tribes (phylae) such as Achaians, Dorians, Ionians, etc.In 212 AD the Roman emperor Caracalla gave people from Roman provinces equal rights to those of the citizens of Rome and the right to call themselves "Romans". The name Hellenes, which by then had become a synonym of attachment to old religions, was replaced by the name Roman.
The name Hellenes began to mean Greek again around the 11th century AD. when the Byzantine Empire was already a "Greek state", although preserving the name "Eastern Roman Empire".
During the Ottoman occupation of Greece (1453-1828) the Christian inhabitants of Greece were again called Romans (Rhomioi). This name is still in everyday use.
After the independence of modern Greece from the Ottoman Empire the new founded country was named officially "Hellenic Republic" (or 'Hellas") and the people "Hellenes". The name by which the country and the people are broadly known, though, is Greece and Greeks respectively.