Greece says the name "Macedonia" implies a territorial claim over its own northern region of that name. Row between the two countries has blocked the ex-Yugoslav republic's attempts to join NATO and EU.
Tens of thousands of flag-waving Greeks gathered in the northern city of Thessaloniki on Sunday to demand that the Republic of Macedonia change its name because it's also the name of the Greek province of which Thessaloniki is the capital.
Greece and Macedonia, which share a border, have been locked in the name dispute since the republic declared independence from Yugoslavia in 1991.
Greeks feel the use of the name "Macedonia" is a usurpation of their heritage and implies territorial claims on their province.
Macedonia is represented in international organisations as The Former Yugoslav Republic of Macedonia (FYROM) and is seated in the United Nations (UN) under the letter T, right after Thailand. Greece successfully vetoed Macedonia's application to join NATO in 2008.
Some minor scuffles erupted between the protesters and anarchists who had organised a counter-demonstration, prompting police to intervene with tear gas.
The rally drew members of the neo-Nazi Golden Dawn party who had gathered around the statue of Alexander the Great along with local clergy.
No public official was among the five keynote speakers.
Several local lawmakers attended, as did the local bishop, Metropolitan Anthimos of Thessalonica, whom many people consider the real leader of the nationalist hardliners opposing an accommodation between the countries.
Anthimos, in speaking about the citizens of Macedonia, used the term Skopje, the name of its capital, which is how most Greeks refer to them.
Police said more than 90,000 demonstrators had joined the protest in Thessaloniki, organised by hardline clerics, far-right leaders and Greek diaspora groups.
Protest leaders said at least 400,000 people had turned up.
"We estimate there were at least 400,000 people. It is impressive," rally organiser Anastasios Porgialidis said.
Police said 284 buses had transported people from around Greece to the port city.
The rally didn't reach the magnitude of one in 1992, when the name issue first flared up. It was prompted by recent efforts on both sides of the border to find an acceptable compromise.
The defeat last year of Macedonia's nationalist conservatives by the social democrats has improved the climate, and Macedonian prime minister Zoran Zaev accepted the invitation by Thessaloniki mayor Yannis Boutaris, an outspoken anti-nationalist, to spend New Year's in the city.
But those who took part in the rally would have none of it.
"Today, the message is aimed primarily at Greek politicians," said Giorgos Tatsios, president of the Greek Federation of Macedonian Cultural Associations. "Those who use the name of "Macedonia" and give it away with no scruples. We call on the government and, especially, the foreign ministry and (foreign minister Nikos) Kotzias to become the hero of Greek Macedonians and not hand over the name. If he does, he should know he is a traitor to the nation."
People presumed to be right-wing extremists set fire to a building occupied by some of the anarchist counter-demonstrators in the centre of the city. The building suffered extensive damage, but none of its occupants was present when masked men set fire to it.
The constitutional name of the country is the Republic of Macedonia and the short name Macedonia when referring to it. More than a hundred countries accept as its constitutional name. But in the international organisations such as UN, EU and NATO the country is referred as FYROM.
Macedonia repeatedly said and put an article on its constitution that it does not have any territorial claims with its neighbours. It also changed its national flag that used to be a sign of Alexander the Great.
The emperor is another dispute between the two nations that cannot share the historical heritage.
Leftist prime minister Alexis Tsipras has said, most recently in an interview published Sunday in Greek newspaper Ethnos, that he wouldn't mind a composite name that includes the word "Macedonia".
But his coalition partner, defence minister Panos Kammenos, leader of the Independent Greeks party, has taken a hardline stance, saying he wouldn't accept the inclusion of the name "Macedonia," suggesting the neighbouring country call itself Vardarska.