In Krutha Yuga, when King Suparsha was searching for a suitable place to do penance & get moksha, He came across this cave & found it suitable. This was the reason to name this cave after king suparsha.
King Suparsha prays lord Shiva to bless him to do penance without any hurdles. Lord Shiva appoints one of his ganas bhairava to permanently stay at the entrance of the cave to make sure that king's penance is not disturbed. It is also said that lot of Rishi's and Maharajas have come to this cave to do penance and one among them is Sri Sridhara Swamiji of Varadapura. This is about 2 kms from the temple on Halli Hole road. At the entrance of the cave, Bhairava swamy idol is worshiped. A liitle down in the cave towards left are the 3 separate lingas - it is also called tri-shakti linga - kali, Lakshmi, Saraswathi.