ATHENS — A landmark agreement to change the name of Macedonia and end a decades-old dispute with Greece appeared to be on track on Friday, but it was becoming increasingly clear that few people in either country were terribly happy about it.

The announcement of the agreement on Tuesday prompted the main conservative opposition party in Greece, New Democracy, to call for a vote of no-confidence against the government of Prime Minister Alexis Tsipras, plunging Parliament into an acrimonious debate that forced Mr. Tsipras on Friday to abandon plans to brief lawmakers on the naming deal.

Greece has long objected to its northern neighbor’s use of the name Macedonia, arguing that it implies territorial aspirations against a northern Greek region with the same name, and represents an attempt to appropriate the ancient civilization of Macedonia, the center of the kingdom of the Greek warrior king Alexander the Great.

There have also been more far-reaching implications: The dispute has kept Macedonia out of the European Union and NATO.