"The vote on constitutional amendments that changed the name, identity, history and culture was done against the constitution".
Eighty-one deputies in the 120-seat parliament voted in favour.
Ethnic Albanians make up about a quarter of Macedonia's 2.1 million people.
The debate on January 11 followed a postponement a day earlier, with Prime Minister Zoran Zaev and his allies negotiating with lawmakers opposed to the change.
Delays had marked the October vote that launched the procedure to change the constitution, also with a two-thirds majority.
The deal encountered strong opposition from both sides of the border, with critics saying it offered too many concessions to the other side.
Opponents of the agreement, mostly supporters of the opposition conservative VMRO-DPMNE party, were holding a peaceful protest late Friday outside parliament in Skopje, the capital.
Mickoski told reporters the move Friday to change the country's name to North Macedonia to appease neighboring Greece was made against the desires of the Macedonian people "and is an act of treason".
Zaev agreed on the name change with Greek counterpart and fellow leftist Alexis Tsipras in June.
"My sincerest congratulations to political actors and citizens of the hopefully soon to be North Macedonia on parliament's vote on the constitutional changes", Hahn tweeted.
The name change follows an agreement with neighboring Greece, which in turn is bound by the terms of the deal to remove its objections to Macedonia joining North Atlantic Treaty Organisation and then potentially the European Union.
But a change of government in Macedonia in 2017 finally brought the start of serious negotiations, which led to the deal reached a year ago.
Greece has blocked that path since Macedonia broke away from the former Yugoslavia in 1991 because, it says, the name Macedonia should apply exclusively to its own northern province.
When Macedonia declared independence during the break-up of Yugoslavia in 1991, Greece objected to its new neighbour's name.
Greek Prime Minister Tsipras has said he wants to bring the deal - which has brought his coalition government to the brink of breakup - to parliament in coming weeks.