Greece has every business to oppose the name, it is within the UN rules for a country to call itself whatever it wants as long as it doesn't offend anyone else, and quite frankly it offends many Greeks for a country having no business with the name "Macedonia". Tito renamed the area in the 40s to start a dispute with Greece to gain access to the Aegean. Communist propaganda goes a long way...
Think about this then, a country that has around 30% of a region, not even the Ancient region (which is 90% within Greece) but with Ottoman drawn borders, calls itself "Macedonia", of which Greece has 50% of that region, and then claims Alexander the Great (names the airport Alexander the Great airport - wtf), plans to build a 30metre statue in the capital Skopje (not even in the Ottoman drawn border region of Macedonian), claims Thessaloniki (they use the Bulgarian name Solun and call it their capital) is occupied by the Greeks (Serbia, Greece, Bulgaria, Ottoman Turkey fought in WWI, where is this "Macedonia" in these battles?), speak a Slavic-Bulgarian dialect, call their language "Macedonian", claim the "Macedonians" were expelled from Greece (were actually Communist traitors, some even Greek and still hold a grudge, for example Prime Minister Gruevski's grandfather fought for Greece and family want their property back after being exiled for being Communist traitors)... the picture that starts to unfold are a lot of people (not all) that use Greece as excuse for their problems much like most of the Middle East use Israel as a root of all evil.
Besides, Greece can wait this out, FYROM, which is 1/4 Albanian can't wait it out forever and when/if the current PM is gone the issue will be resolved.