The moniker, a reference to “Donbas” and “Donald,” was described by four people familiar with the negotiations, who all spoke about it on the condition of anonymity because of the secrecy surrounding them.

When a Ukrainian negotiator first mentioned the term, partly in jest, it was as part of an attempt to convince the Trump administration to push back more against Russia’s territorial demands, according to three of the people familiar with the talks. President Vladimir V. Putin has vowed to keep fighting until Russian forces reach a key administrative boundary on the edge of the Donbas, the industrial region in eastern Ukraine where the Kremlin first started waging war in 2014.

That a name evocative of Disneyland has been applied to a depopulated, decimated swath of Ukrainian coal-and-steel country could appear jarring as Europe’s deadliest fighting since World War II continues to rage. But it also reflects a global reality in which governments appeal to Mr. Trump’s vanity in order to get American might on their side.