The Kashi Khand of Skand Mahapuran has narratives that give full coverage to the story of origin of the idols of various gods and goddesses, especially of the various lingams that prominently dot the cityscape. In its eighty-fifth chapter there is the story of how Durvaseshwar/Kameshwar Mahadev came into being. As the name suggests, Lord Shiva bears the name of his devotee here. He is the ‘Lord of Durvasa‘. For those who do not know much about the sage famous for his irascibility, fiery temper and powers, rishi Durvasa directly originated from Lord Shiva. He is a great devotee of Lord Shiva and is full of praise for the city of Kashi as he reaches there. He likes the city and starts his austerities to please his Lord in order to get a boon he wants. Time passes but the sage has no success.
Irascible as he is, he decides to curse the city that does not bring the fruits of his devotion and austerity to him. The fire of his anger envelops the sky, and since then it looks blue. The ganas of Lord Shiva who reside in his beloved abode get agitated and angry and take countermeasure by creating a huge wall all around the city that does not let even fire pass. The world burns and Kashi is breathless. Lord Shiva is pleased with the powerful sage and appears before him (I will not digress and write of another lingam that came to earth at this point of time).
On seeing his lord Durvasa becomes aware of what he had done. He is full of shame and remorse to have thought of cursing Mother Kashi, but Lord Shiva is happy with him and asks him to ask for his boon. The sage asks for only one boon, that the lingam he established there fulfills the desires of the devotees, hence known as the Lord of Desires, also that the water of the pond may have similar powers. Lord Shiva was pleased with the selfless sage and called the lingam Durvaseshwar before granting the sage his boon. He also declared that the most auspicious day for the devotees to reach there would be the thirteenth day of Pradosh that coincides with Saturday.