Indeed, at a moment when the bloc of nations is facing a raft of challenges, Friday night’s vote was viewed as a rare bit of good news and a triumph of diligent diplomacy. But there is still more work to be done.

Even before the vote in Skopje, a rift seemed to be growing over the issue between Prime Minister Alexis Tsipras of Greece and his right-wing coalition partner, Panos Kammenos.

Mr. Kammenos has threatened to leave the government, a move that could potentially force early elections.

While he has grown increasingly vocal, it is unclear if he will make good on his threat.

If Mr. Kammenos were to walk away, he would abandon his current job as defense minister with no guarantee that he would be able to prevent the name change from going through.

In a television interview on Wednesday, Mr. Tsipras said he was confident that Mr. Kammenos would continue to back the government, but he added that he would seek a vote of confidence in case his right-wing partner withdraws, saying he was certain he could secure the support needed to stay in power.

Mr. Tsipras also suggested that, should Mr. Kammenos withdraw, he would call snap elections rather than lead a minority government. He said that although the Greek Constitution would allow him to continue to rule with a minority government, “politically” there would be a problem.

In any case, he said, a snap election would take place after the Macedonia deal is ratified in the Greek Parliament and following the completion of some pending issues.