The above image is of my Greek national ID card, which I had to carry on my person while I lived in Greece. It was issued on September 27, 1969, in Nea Smyrni, Greece.
It is interesting that on the upper right corner it states that it is the Kingdom of Ellas. Both are “correct” depending on the language and context. Hellas, Έλλάς, (or Ellada/Ellas) is the correct endonym (native name) used by Greeks for their country, while Greece is the correct exonym (foreign name) used in English and derived from Latin. The official name is the Hellenic Republic, or Elliniki Dimokratia.
[From Wikipedia] The English name Greece and the similar adaptations in other languages derive from the Latin name Graecia (Greek: Γραικία), literally meaning ‘the land of the Greeks’, which was used by Ancient Romans to denote the area of modern-day Greece. Similarly, the Latin name of the nation was Graeci, which is the origin of the English name Greeks. Those names, in turn, trace their origin from Graecus, the Latin adaptation of the Greek name Γραικός (pl. Γραικοί), which means ‘Greek’.
The Romans most likely called the country Graecia and its people Graeci