The etymology of "Peru" is debated among historians and linguists. Three main theories exist:
From the Quechua word Birú (or Pirú), meaning "river" or specifically the Birú River (modern Chira River in northern Peru). Early Spanish explorers (Andagoya, 1522) heard local chiefs refer to a powerful cacique or region as "Birú." The name migrated south with Pizarro's conquest.
The Virú Valley (north coast) hosted the Virú (Gallinazo) culture (200 BCE–600 CE). The name "Virú" may have been generalized by Spaniards to the whole region. Linguistically plausible (Quechua wiru = "twisted/winding" – river).
Chronicler Pedro Cieza de León (1553) wrote: "The name Peru comes from a great lord called Berú, who governed near the river of San Miguel (Chira)." Similarly, Inca Garcilaso de la Vega mentions a chief Pelú. This reflects the Spanish pattern of naming lands after local rulers (e.g., Chile ← Tili, Colombia ← Colombo).
Consensus leans toward Birú/Virú (geographic) as the ultimate root, filtered through a local leader's name.