It's a controversial and long-running dispute that has derailed attempts by FYR Macedonia to join the EU and NATO.
But what's it all about and why does it incite such strong reactions in both Greece and the Former Yugoslav Republic of Macedonia (FYROM)?
What’s the dispute about?
FYROM is controversial for Greeks because it uses the same name as a neighbouring region in northern Greece.
Athens claims the region Macedonia, which lies just across the border from FYROM, has used that name since the times of Alexander the Great.
There are also concerns that agreeing to FYROM would lead to Skopje having territorial claims to the region.
Why is the issue in the news?
The election last year of FYROM's pro-EU prime minister, Zoran Zaev, helped push the issue towards resolution.
“There is a greater commitment by the Macedonian government to talk about it and there is a sense of sincerity about wanting to resolve it,” Professor Florian Bieber, an expert on Balkan politics from the University of Graz in Austria, told Euronews. “And there have been positive signals coming out of Greece as well.”
The two countries reached an agreement in June to rename the country the Republic of Northern Macedonia.
Other names under consideration had been: Republic of New Macedonia; Republic of Upper Macedonia; Republic of Vardar Macedonia; and Republic of Macedonia (Skopje).
How did the dispute come about?
The name dispute was an issue between Belgrade and Athens before the 1990s, when the People's Republic of Macedonia made up part of Yugoslavia.
But it really came to prominence in 1991 when FYROM declared its independence from Yugoslavia.
So everything's settled then?
No. Hopes of a swift resolution to the long-running dispute looked optimistic in the days after the agreement.
FYROM's president, Gjorge Ivanov, said he would not sign the deal claiming it violated the constitution.
"My position is final and I will not yield to any pressure, blackmail or threats. I will not support or sign such a damaging agreement," he told a news conference.
Ivanov, who as president has the backing of the nationalist opposition VMRO-DPMNE and has the right to veto the deal, said FYROM's possible future membership of the European Union and NATO was not sufficient excuse to sign such a "bad agreement".
There is also opposition to the agreement in Greece.
An opposition party filed a no-confidence motion against Prime Minister Alexis Tsipras over the deal.
The prospect of an agreement between the two countries has also had people out on the streets in recent weeks.
There were protests in northern Greece in early June and by several thousand supporters of the VMRO-DPMNE party in FYROM.
What happens next?
The deal between the two countries is set to be signed by Greek foreign minister Nikos Kotzias and his Macedonian counterpart Nikola Dimitrov on Sunday (June 17) morning.
But it will still require ratification by both national parliaments and approval by referendum in FYROM, which is not assured.