Answer by taking a quote from the following article:

The Greeks (Greek: Ellenes) have been identified by many ethnonyms. The most common native ethnonym is "Hellen" (Ellen), pl. Hellenes (Ellenes); the name "Greeks" (Latin: Graeci) was used by the Ancient Romans and gradually entered the European languages through its use in Latin. The mythological patriarch Hellen is the named progenitor of the Greek peoples; his descendants the Aeolians, Dorians, Achaeans and Ionians correspond to the main Greek tribes and to the main dialects spoken in Greece and Asia Minor (Anatolia).

The modern English noun Greek (Old English Grecas or Crecas) is derived from the Latin Graeci, which in turn originates from Ancient Greek Graikos (Graikos). It seems that the word is related with the Greek word geron geron, "old man" (from the PIE base *gerh2-, "to grow old") via Proto-Greek *gera-, "old age"--also related to Mycenean Greek kera /geras/, "gift of honour". The Germanic languages borrowed the name with an initial k sound, which was probably their initial sound closest to the Latin g (Goth. Kreks).  Aristotle used the term Graikos related with Hellenes (Meteorologica I xiv) and claimed that it was the name originally used by the Illyrians for the Dorians in Epirus from Graii native name of the people of Epirus. He places Ancient Hellas in the region of Achelous river around Dodona where in his opinion the great deluge of Deucalion must have occurred. The priests of Zeus in Dodona were called Selloi which could lead to Sellanes (like Akarnanes) and then to Hellanes-Hellenes. However the toponyms and the Greek tradition indicate that it is more possible that the homeland of the Greeks was originally in central Greece and that the name was probably Pre-Dorian. A Greek legend is referring to an older deluge of Ogyges in Boeotia, in the region occupied by the Minyans which are considered autochthonous or Proto-Greek speaking people. The region outside of Attica including Boeotia was called Graike and the word Ogyges related with ocean came to mean "from earliest days." Homer is referring to Hellenes as a relative small tribe in Phthia in central Greece (Achaea Pthiotis). In the Parian Chronicle is mentioned that Phthia was the homeland of Hellenes and that this name was given to those previously called Graikoi (Graikoi). In Greek mythology, Hellen, the patriarch of Hellenes, was son of Deucalion (who ruled around Phthia) and Pyrrha, the only survivors after the great deluge. Hesiod is referring to Graecus son of Pandora, who was sister of Hellen. Alcman mentions that the mothers of Hellenes were Graikoi.  The German classical historian Georg Busolt (1850-1920) derives the name from Graikos,"inhabitant of Graea, a town on the coast of Boeotia. The name Graea (graia) is derived from Proto-Greek grau-j-, "old lady". Homer, while reciting the Boeotian forces in the Iliad's Catalogue of Ships, provides the first known reference to a region named Graea, and Pausanias mentions that the ancient city of Tanagra was for a time called Graea, adding that "no one knows where this Graia really was; Aristotle thought it was near Oropus, further east on the same coast as Delion." Busolt claimed that the name was given by the Romans originally to the Greek colonists from Graea who helped to found Cumae the important city in southern Italy where the Latins first encountered the Greeks and then to all Greeks.  According to Rene Olivier, in the French language the word grec (Greek) is sometimes also used as an ethnic slur meaning fraudster (in contrast with hellenique which has no negative connotations).

What is something interesting you can tell me about the Greeks?
The modern English noun Greek (Old English Grecas or Crecas) is derived from the Latin Graeci,