But the decision is not universally supported.
Macedonian and Greek ministers on Sunday signed a landmark agreement aimed at finally resolving their decades-long dispute - which Macedonia's PM said had "turned an enemy into a friend". Officers responded with tear gas and flash grenades. Several demonstrators complained of breathing problems.
A Reuters witness saw protesters throwing stones at police and chanting, "Macedonia, Macedonia we will give our lives for Macedonia".
Tsipras could also face ratification problems, with his junior governing partner, the Independent Greeks party, and the centre-right New Democracy party, both against the deal.
Specifically, by officially recognising a Macedonian language and nationality, it is nearly certain that the country will be called Macedonia by the broader world, instead of North Macedonia, opponents of the deal argue.
Foreign ministers of Greece, Nikos Kotzias (centre) and Former Yugoslav Republic of Macedonia Nikola Dimitrov (left) and Greek Prime Minister Alexis Tsipras. "Our countries are leaving the past behind and are looking to the future".
"In our official communication, we will continue to refer to this country as the Former Yugoslav Republic of Macedonia, and this is what we have been doing until now", she added. Negotiations took place under United Nations auspices beginning in 1995.
After nearly three decades of dispute, the northern neighbour of Greece should soon become North Macedonia.
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This came as no surprise, as Orban sent a video message to an anti-deal rally in Skopje held by the opposition VMRO-DPMNE party, praising its refusal to bend "under pressure from foreign powers", Beta news agency reported on June 4.
Skopje hopes to secure a date to begin European Union accession talks at an European Union summit on 28-29 June and an invitation to join North Atlantic Treaty Organisation on 11 July.
Macedonia will still have to make about 150 changes to its constitution and the agreement must be approved by the parliaments of both countries before it can go into effect.
Greece insisted on a name change for years, arguing that the name Macedonia implies claims on its own northern province of Macedonia, and on Greece's ancient heritage.
Tsipras survived a no-confidence vote mounted by Greece's opposition in parliament on Saturday, but the depth of public emotion against the deal is strong.
Macedonians are not the only ones enraged by the deal. On Sunday, Greek police fired tear gas at a crowd protesting on their side of the border, not far from the signing ceremony. The Macedonia's president has also vowed to block the deal.
Macedonia was admitted to the United Nations in 1993 under the provisional name of the "Former Yugoslav Republic of Macedonia", but more than 120 countries including Russian Federation and the United States have recognised the Balkan country under the name of "Republic of Macedonia".