Re: History of city names
Banaras is a corruption of the original Varanasi. North Indians have changed it to Banaras. In the south we still call it Kashi or Varanasi not banaras. 
It was supposedly founded by Lord Shiva. In the Rig Veda, it is referred to as Kashi (“the luminous one” as an allusion to the city’s historical status as a centre of learning, literature, art and culture).
Varanasi has its origin from the river Varuna which is a tributary of the river Ganga and flows through the area and the other river Assi(another tributary of Ganga) has now dried up or gone underground though a small stream of Nalla near Assi Ghat is considered as Assi River.