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. where the Byzantine Empire was already a "Greek state".
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.