Here is a deeper definition for those interested in the truth.
Greece: The name given to the inhabitants of the small nation that revolted against the Ottoman empire, around 1821. This name was arranged by non-Greeks and is the one used in the english language, meaning primarily by anglosaxon countries. "Greeks", call themselves today Ellines (Έλληνες) and their country "Greece", Ellas. Of course, these words are probably best written in english as Hellas and Hellenes. I am not writing them this way, because in the past i was astonished to see that an American woman argued with me in blaming Greeks of the past for a generalized trend of homosexuality, saying: "So why do you all call yourselves Hellenes?" You get it? She was telling me that since we call ourselves Hellenes, it must be related to the female name of Helen, so yeah, we got to be gay! I was really amazed at that level of intellectual confrontation. Which reminded me once again how easily Greek words can and are misunderstood when transfered into english. By the way, yes, Helen is a Greek female name, and it comes from the same root word as Hellas and Hellenes. But no, Greeks do not name themselves collectively with that female name..
Lets get into more details on the name. Greeks, were called the first settlers of the south Italian colonies of Greeks in classical times, by the Italians of the time. Then it passed to all latin-based languages. Before that? Yes, Homer refers to Greeks as one of the Hellenic tribes that took part in the Trojan War. This tribe came from Boiotia (region in Greece).*
With the formation of the independent state in the 1800s, there was a debate inside Ellas too, about how its inhabitants should call themselves from now on. There were different opinions. Three actually. 1. Greeks, the name with the history i mentioned, which was what foreign powers wanted to use. It was in very minor use in the 'Greek' population of the time, mostly to declare they are not Turks. There are few accounts of non-educated warlords of the 'Greek' countryside, that declared 'we are Grecians', 'i was born a Grecian, i will die a Grecian', etc. 2. Romioi, a word related to 'Romans'. It heavily declares mostly the Orthodox Christian religion of the population, than their nationality. Considering the 1000 year old Eastern Roman Empire's (Byzantium) legacy, that 'Greeks' were a part of, and the 400 years under Ottoman rule where Christianity was their main concept of coherence and unity against the muslim Turks, it is not a suprise that this name was also considered. 3. Ellines (Hellenes), a name that clearly states nationality, the name that from the classical times was used to first show signs of unity between the 'Greek' tribes.
The last one was chosen, and the independent nation was first named "Hellenic Kingdom".
But, non-Greeks continued and continue to call the nation 'Greece'. Thus, we are discussing now in a node named 'Greece'.
It is probably a non-issue to anyone but people of the said nationality. But a deeper history of the name is interesting, at least to the ones interested in historical truth.
*This is only one possibility for where the words 'Greeks' and 'Greece' originated. There are numerous different opinions, by different ancient writers. It would be extremely lengthy to include them all here.