[mjn]

The argument is more caused by disputes over history than by the name duplication (though there is some dumb arguing over just the name). What mostly inflames Greek opinion is the other set of claims that goes along with the name: for example, a number of historians from the Republic of Macedonia claim that the ancient Macedonian language was a Slavic language (rather than a Greek dialect), and that the people of the modern Republic of Macedonia are the modern cultural descendants of the ancient Macedonians. Whereas Greeks see the ancient Macedonians as part of their own ancient history, like the Ionians and Athenians and Minoans and other Greek peoples. Also a particularly important part of it due Macedonia's role in instigating the Hellenistic age. Third-party historians generally side with the Greek view (Slavic migration to the Balkans far postdates the ancient Macedonians). But the use of the name by the Republic of Macedonia, especially together with its use of ancient Macedonian symbols, and unorthodox historical claims made by some of its leading figures, does seem to have confused some laypeople, which annoys Greeks, who feel some of their history is being appropriated.

Purely geographically speaking, just about anyone vaguely in the region does have a claim to be in Macedonia, because it's been the name of a number of territories over the years [1]. The real dispute is more over cultural legacy than whether Skopje or Thessaloniki are more geographically "in" Macedonia.

[1] A decent concise summary: http://en.wikipedia.org/wiki/Macedonia