The Amazon River is named after a Greek legend, because a Spanish chronicler said women fought his expedition on its banks.
The trip was never meant to go that far. Gonzalo Pizarro sent his second in command, Francisco de Orellana, down the Napo River with about fifty men. The hope was that they would find provisions and bring them back. They never returned. On 26 December 1541 the men chose Orellana to lead a new expedition, and they kept going downstream. They reached the Atlantic on 26 August 1542.
The friar Gaspar de Carvajal kept the chronicle. Wikipedia dates the key fight to 24 June 1542, as the boats approached the Trombetas River. Carvajal wrote that women led the warriors. In one English translation, they were "very white and tall, with very long hair braided and wound about their heads." Each was "doing as much fighting as ten Indian men."
To Spaniards who knew the classics, that meant the Amazons, the warrior women Herodotus placed in Asia. Orellana called it "the river of the Amazons."
It already had European names. Explorers at its mouth had called it Río Santa María del Mar Dulce, "sweet sea," because its fresh water pushed far out into the ocean. Europeans also knew it as the Marañón, a name still used for a stretch in Peru.
Nobody knows who the warriors were. Etymonline mentions women of the Tapuya, and also a view that they were long-haired, beardless men. It records a rival theory too: that the name is a corruption of a Tupi or Guarani word meaning "wave." Historians long dismissed Carvajal's chronicle as exaggerated, though Wikipedia notes that later research supported his reports of a flourishing civilization along the river. The warrior-women account remains the standard explanation of the name.
The Greek word carries its own myth. A long-standing folk etymology splits Amazon into a-, "without," and mazos, "breast." From that came the story that Amazons removed one breast to draw a bow more easily. Etymonline calls this folk etymology. It says the word probably came from an unknown non-Indo-European language, or perhaps from an Iranian compound meaning "(one) fighting together."