How did ancient peoples identify themselves?

[Tiberius Nero]

Also, how did the Macedonians and the Greeks view themselves? Were they primarily Makedones, Athenai, Epeirotes etc, or was there a Hellenic identity above that? If so, was it stronger or weaker than their local identity?

Local identity certainly took precedence; there was a concept of "Greekness", but didn't really mean much on the political level; when not faced with a common enemy one Greek city could very well receive financial aid from non-Greeks (Sparta in the Peloponnesian War e.g.).