Have you ever wondered why Greeks speak of themselves as "ellines" while the whole world refers to them as "Greeks' ?I have so here is what I managed to find out.
As everything else in Greece the things are complicated so try to focused :P. The name "Hellenes" comes from a small tribe in Thessalia. Homer describes it as having beautiful women and brave warriors". Another thing we know about them is that during the Trojan war, they fought along side the Myrmidons under Achile's command.
Now, about the name itself, "Hellines", nobody actually knows how it came to being and where from but there are a lot of suppositions. Some say it comes from the name of Zeus's priest called Selloi that in time became "Sellanes" and than "Hellenes" others argue that the name means "the land of sun and stone" from the "Hellios" which means sun.
About the origins of the term "greek", Aristotle is one of the first ones to use the term "graikos" while referring to Hellines. He says that's the name with which the Illyrians refered to the Dorian people. As a meaning, the historians believe that it's related to the term "geron" which means "to grow old" or "old age".
A third name that the Greeks are called, outside their country that is, is Yaunas (Yunas). When the Persians came to Asia Minor they found there the Ionians and they called them Yaunas. Today, in the Arabic countries Greeks are referred to as Yaunas (Yunas).
Basically, whomever came into contact with the Greeks took the name of the tribes they've encountered, not the name of the nation.The Romans came from the west and they encountered the Dorians which were called "graikos". That's how the Latin word "graeci" came to being. Than the Persians came from the east and encountered Ionians. In the north of the country there are also the Macedonians who are Hellines non the less but also Makedonians.
Now the easiest of the questions remains: How come all western countries we know call Hellines Greeks? That is very easy. The Roman Empire stretched far and wide and made commerce with whole known worlds at that time. Every nation who got to know the Greeks at that time, got to do that through the Romans thus adopting their way of calling them.
I hope this sheds a bit of light on the subject.i don't know about you but the question bugged me for a while now:)