Argentina is named for silver that was mostly somewhere else. The riches behind the name lay in mines in what is now Bolivia.
The story starts with a failed voyage. In 1516 the Spanish navigator Juan Díaz de Solís explored a huge estuary on South America's Atlantic coast. He called it the Mar Dulce, the "freshwater sea." Some boats from his expedition were wrecked off Santa Catarina Island in present-day Brazil. Among the survivors was Aleixo Garcia.
Living with the Guaraní, Garcia heard tales of a "white king" to the west who ruled cities of great riches. Europeans came to speak of a Sierra de la Plata, a "silver mountain range." In 1524 Garcia set out westward and reached the edge of the Inca Empire. He sent back messengers carrying roughly 40 kilograms of silver before he was killed in 1525.
Between 1526 and 1529 Sebastian Cabot explored the estuary and its rivers. He traded with the Guaraní for silver objects, and he is widely credited with renaming the estuary Río de la Plata, the "River of Silver." English still calls it the River Plate, using an old sense of "plate" for silver.
The silver was real, but it was not there. The great deposits were at Potosí, far to the northwest in modern Bolivia. Buenos Aires grew up partly as an outpost guarding the route for that Potosí silver.
The Latin form came next. Argentum is Latin for silver, and argentinus means "of silver." A Venetian map of 1536 already uses the word Argentina for the region. Martín del Barco Centenera gave it its first known printed use in a poem published in Spain in 1602. In 1612 Ruy Díaz de Guzmán called the territory Tierra Argentina, "Silvery Land."
After independence, the 1826 constitution used "República Argentina." On October 8, 1860, President Santiago Derqui made that the official name.
So the country and its great river carry the same name in two languages. Plata is the Spanish word for the metal. Argentina is the Latin one, borrowed to give a young nation a name with classical weight.