Mycenaean Greeks - clearly Greek, and considered as such by classical Greeks. Linear B = Greek dialect. Language remained in Peloponnese as Arcado-Cypriot (compare Linaer B inscriptions). Called themselves Achaeans/Danaans/Argives. Collapse of culture, then relative vacuum?
Dorian invasion? Certainly spread of Doric/Ionic/Aeolic dialects into the Peloponnese, displacing Linear B/Arcadian to Arcadia.
Foundation myths in the Archaic/Classic period - not necessarily consistent, often confusing. Hesiod's "Catalogue of Women" - Deucalion & Pyrhha, Hellen, Aeolus, Dorus, Ion and Xuthus. Mythical founders of the Hellenes.
Herodotus, Pausanias, Thucydides etc.: Distinction between Hellenes (accepted as later immigrants to Greece) and Pelasgians (there in the first place). Hdt - Pelasgians: Arcadians, Achaeans, Atticans, Aegialans (-> Ionians (I 56 especially)). Ionians took name from Ion, but not descended from him.
Arcadians, Achaeans -> clearly Greek (referred to by Homer, spoke Linear B etc. etc.) So why did Classical Greeks consider them to be non-Hellenic? First reference to Hellenic meaning all Greeks relatively late, so perhaps the distinction was maintained longer than appears.
In Homer, Hellas small region in Thessaly. Very little mention of Dorians, Ionians or Aeolians (and certainly not in the later sense). SO: was the Dorian invasion (and associated changes) a real event in which tribes from central Greece (e.g. Hellas) expanded into a rather vacant Peloponnese and other parts of Mycenaean Greece? And does therefore the Hesiodic myth of the sons of Hellen reflect these real events?
The Hellens called the older (more settled) Greek populations Pelasgians, and themselves Hellenes (Dorians, Ionians etc.)? Then gradually, due to the dominance of the Hellenes, the name came to be used for all Greeks? This is more-or-less what Thucydides says (I, 1).