The lake Is actually separated by a narrow strait of land into two distinct bodies of water and each has one name for those in Bolivia and a different name if you're in Peru.
In the midst of the Bolivian portion of the lake, off the shore from Copacabana, lies Isla del Sol (Island of the Sun). The island has ruins dating back to the Inca civilization some 2200 years before Christ. Most of the ruins, however, date from the 15th century Incan emperor known as Topa Inca Yupanqui (Noble Inca Accountant). The ruins include a labyrinth from which they draw the name "Chincana" -- "the place where one gets lost."
According to some students of the site, Lake Titicaca was a site sacred to the Incas. In the Incan creation myth, the god Con Tiqui Viracocha rose up out of Lake Titicaca. After commanding the sun (Inti), moon (Mama Killa) and the stars to rise, Viracocha created more human beings by speaking life into stone and command his creation to populate the world. The Incas therefore believed that Lake Titicaca was their place of origin, and that upon death, their spirits would return to this lake.