From the Hellenic Society at Manchester University:

According to some:
Around 635BC citizents from Kimi, Evia with some people from Grea, Viotia (perhaps the place today known as Tanagrea) founded a new Hellenic Colony in Italy with the name Nea Polis ( which means New City, later to be known as Napoli, or Naples in English ). This was the very first time that the Latins came close to the Hellines and thus named them 'Greques' after the citizents of Grea. The names Hellas and Hellines are the names the inhabitants of this small peninsula of the eastern Mediterranean use for their country and for themselves respectively. Thus the term 'Greek' although derives from a Hellenic word, is artificial and not acceptable and we prefer the term 'Hellas' as it represents better our origins......

According to others:
The first Hellines to be called Greeks ("Graikoi") were from the region of Epirus, in Northern Greece. That was so until the end of the Turkish occupation of Greece. After the revolution and the liberation from the Turks, the new Greek country spanning the regions of todays mainland Greece (Sterea Ellada) and the Peloponnese, was born. The people, at that time, were closer the the term "Graikos" than "Ellinas". However, the Turks were not happy about this fact at all, since it carried dangerous insinuations about the "Graikoi" of the regions of Thessalia, Epirus, Thrace, Minor Asia and Constantinople, who were still living under the Othoman occupation. It was therefore decided to chose the name of "Hellin", which also brought them closer to ancient Greece. The term "Ellin" derives from the ancient greek words "El", which means uncoquerable, unsuperable, and "Lan", which means people.