"We are all republicans according to the first article of the constitution [which declared France a republic]," argued lawyer Christophe Léguevaques who represented the plaintiffs on Tuesday.
But the court decided that there was no "imminent danger" of "major civil, social and political trouble", as the plaintiffs argued.
It declined to rule on the fundamental question of whether the party could use the term, however, and Lèguevaques said that there would probably be an appeal.
They claim that the name indirectly slanders other parties by appropriating a term that is frequently evoked as the essential French political value.
"We'll be the Republicans but you will be republicans," UMP lawyer Jean Castelain told them in court.
The case had been fast-tracked because UMP members will take part in an electronic vote on Thursday and Friday ahead of a special conference to "refound" the party on Saturday.
Sarkozy, who earlier complained that the left is trying to decide what the opposition calls itself, wants to rebrand the party in an effort to close the door on the 2007 electoral defeat and the infighting that followed it.