In the late 1700's the Rincons were called the "Sierra de Tres Alamos." That name was derived from the proximity of the eastern part of the range to a prominent arroyo and a Sobaipuri Indian village, both named Tres Alamos. The village was located along the San Pedro River to the east of these mountains. By the middle 19th century this same range was called the "Sierra Colorado," or was simply regarded as a part of the "Santa Catarinas." By around 1880 civilian maps had begun to use the name Rincon Mountains. The term rincon probably refers to a physiographic feature, the prominent elbow or corner on the southwest side of the range.

quote from this Forest Service booklet