Hellenic refers to being Greek.
Yes, "Hellenic" is an adjective meaning "of Greece, the Greek language, or Greek culture". It comes from the Greek word for Greece, "Hellas", and the Greek word for the Greeks, "Hellenes" (in classical Greek; modern "Ellas").
Hellenic Gendarmerie was created in 1833.
Greek literature. Hellenic means Greek.
Hellenic Cup was created in 1983.
Hellenic Athletic was created in 1958.
Hellenic F.C. ended in 2004.
Hellenic F.C. was created in 1958.
Hellenic Police was created in 1984.
Hellenic Bank was created in 1976.
Hellenic Army was created in 1828.
Hellenic Navy was created in 1828.
Hellenic Seaways was created in 2005.