Its obvious that people answering here are not aware of the history of the Macedonians.
Macedonia was partitioned by the World Powers after world war 1 and world war 2.
One part went to Bulgaria, one to Greece and the other to former Yugoslavia.
(and a very small part to Albania)
Of the 3 main countries to which Macedonia was split, the Macedonians in the former Yugoslavia were allowed to be Macedonian and control their affairs.
But the Macedonians under the other countries were suppressed by those governments.
Once Yugoslavia fell, the Macedonians became independent and they wanted to reunite with the other regions from Greece and Bulgaria, so Macedonia would become one country once more.
And as many have pointed out both Greece and NATO would not like this.
If Greece would lose that area of Macedonia it has, Greece would lose the majority of its Agricultural land, and hence would lose a major revenue from its Agricultural Exports.
SO Greece does not want to lose this.
The Western powers gave Greece this area of Macedonia because this area of Macedonia covers the coasts of the Aegean Sea.
During the Cold War, NATO put many military bases so they can control the
movement of ships of the Soviet Union.
And NATO still needs this to watch ships from Russia (which is the new cold war).
SO NOW going back to the original question:
Why the Macedonians won't change their name ?
Its because they want to be Macedonians, free to choose their name and not
let other countries dictate what name they should have.
The Macedonians feel wronged by what the Western powers and what Western politics have done.
So, they will not compromise on the name.
BUT, in the end since the Western powers are still the major players in the World today, that originally partitioned Macedonia, the Macedonians will probably never get what they want, because the Western powers are the ones that don't want Macedonia to get their name.
You can call it Lilliputian if you want.
But this is just the same kind of politics of the Superpower(s) dictating to the small countries.
Just like the Phillipines having been under USA control for so long, and once they got a leader that wanted to follow their own path, the USA was not happy about it.
So its really about Big Players being bullies to the small guys.