Athens argues that the name Macedonia suggests that Skopje has territorial claims to Greece's historic northern region of the same name.
Both countries returned to the United Nations last week hoping to reach a compromise that could end the 27-year dispute.
On Sunday, tens of thousands of Greeks protested against any deal allowing Macedonia to keep its constitutional name.
Greek Prime Minister Alexis Tsipras and his Macedonian counterpart Zoran Zaev will meet Wednesday on the sidelines of the World Economic Forum in Davos to discuss the issue.
It will be the first meeting between the two leaders, the Greek foreign ministry said.
"We expect progress towards reaching a commonly acceptable solution" at the meeting, Greek government spokesman Dimitris Tzanakopoulos told reporters on Tuesday.
"The solution must be found on the basis of a composite name, with a geographical or time-related definition, which will apply to all, making it clear that nobody has a claim on the lands or history of other peoples," he said.
Home to the port cities of Thessaloniki and Kavala, the northern Greek region of Macedonia was the centre of Alexander the Great's ancient kingdom and is a source of Greek pride.
Greece's objections to its neighbour becoming independent in 1991 as Macedonia -- the name the former Yugoslav province has used since the 1940s -- have hampered the tiny nation's bid to join the European Union and NATO.
Macedonia is currently known in the UN by the provisional name of Former Yugoslav Republic of Macedonia (FYROM), but over 100 countries have recognised it as Macedonia.
"The lack of a solution is what undermines (Greek) interests," Tzanakopoulos said on Monday, arguing that Greek sentiment on the issue was being "exploited" by far-right and ultra-nationalist groups.
'Close on certain issues'
Hardline clerics, far-right leaders and Greek diaspora groups had called for Sunday's rallies, which drew more than 90,000 people according to police.
Protest organisers claimed at least 400,000 demonstrators had turned up.
The Greek government on Monday said the size of the demonstration would not impact the talks.
"I don't think it has a bearing on the negotiations," said Foreign Minister Nikos Kotzias.
He added that the two sides were "close on certain issues" and that the talks were "facilitated" by the EU and the US keeping out.
In 1992, more than one million people -- 10 percent of the population -- joined a rally to proclaim that "Macedonia is Greek".
However a recent survey suggested that a majority of Greeks now back Athens seeking a mutually acceptable solution at the UN talks.
Prime Minister Tsipras told Greek media Sunday: "If there is an opportunity for a solution, it would be a national stupidity not to make good use of it."
However, he also said he understood "the concerns and sensitivities" of northern Greeks.
If a deal is reached, it must be put before Greek parliament for approval, with the government expecting a compromise name to be approved despite opposition within some parties.
According to Macedonian media, five alternatives are currently on the table, all containing the name Macedonia.
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