I was intrigued, so looked it up.
https://www.atlasobscura.com/articles/president-rutherford-hayes-paraguay
Twenty miles north of Asunción, hugging the west bank of the Paraguay River, sits a bustling cattle-ranching hub called Villa Hayes. This dusty city serves as the capital of Paraguay’s Presidente Hayes Department, features a Hayes Primary School, and boasts a statue of its namesake: Rutherford B. Hayes, the 19th President of the United States.
Hayes may be obscure in his homeland, but citizens of this South American nation absolutely revere the long-dead president. “Rutherford B. Hayes is our national hero,” says Maria Teresa Garozzo de Caravaca, director of the municipal museum in Villa Hayes. Kids from across Paraguay take school trips to the museum to view Hayes-themed artifacts, including a life-sized effigy next to an American flag. “They really admire the man a lot,” Garozzo explains. “He didn’t fight any battles here, but he’s in the hearts of all Paraguayans.”
Hayes never visited Paraguay, but he involved himself in the defining moment in Paraguayan history. From 1864 to 1870, Paraguay fought and lost the Paraguayan War against the Triple Alliance of Brazil, Argentina, and Uruguay. It remains the deadliest international conflict in Latin American history. By some estimates, Paraguay lost 70 percent of its pre-war population and 90 percent of adult males. It also hemorrhaged huge chunks of its previously claimed territory, and didn’t want more bloodshed to try and wrangle them back.
That’s when President Hayes, a Republican who once graduated from Harvard Law School and practiced law in Ohio, tiptoed into the picture. In 1878, when there was no United Nations or World Court, the governments of both Argentina and Paraguay tapped him to arbitrate a protracted dispute over a large swath of the Gran Chaco lowlands, between the Pilcomayo and Verde Rivers. At the time, these prickly shrublands were home mostly to indigenous communities such as the Guaycurú, Lengua, Wichí, Zamuco, and Tupí-Guaraní, which were losing their ancestral lands to colonizers and had little allegiance to either government. The Gran Chaco was so hot and arid that European settlers often referred to it as “the Green Hell.” Nevertheless, when Hayes, a neutral third party, ruled in favor of Paraguayans in 1878, he essentially bequeathed them about 60 percent of their current land, much of which now bears his name.
Hayes essentially ensured Paraguay’s survival as a nation and is the reason they exist at all.