Why does Paraguay have a department named after US President Rutherford B. Hayes?

The South American nation of Paraguay is divided up into administrative units called departments, in much the same way as the USA is divided up into states. One of these departments is called Presidente Hayes, named after Rutherford B. Hayes, the nineteenth President of the United States.
The territory is named after Hayes because he awarded it to Paraguay after the bitter war between that country and the so-called Triple Alliance, consisting of Brazil, Uruguay, and Argentina. President Hayes acted as an arbitrator in a boundary dispute between Paraguay and neighboring Argentina, and the department that now bears his name was given by him to Paraguay in 1878. In gratitude for Hayes's intercession, the Paraguayan government renamed the department as Presidente Hayes, and its capital city as Villa Hayes.