The name Hellenes seems to be older and it was probably used by the Greeks with the establishment of the Great Amphictyonic League. This was an ancient association of Greek tribes with twelve founders which was organized to protect the great temples of Apollo in Delphi (Phocis) and of Demeter near Thermopylae (Locris).
Is the name more ancient than other group names in the area ?
The name Hellenes seems to be older and it was probably used by the Greeks with the establishment of the Great Amphictyonic League.