The place is open for worship practically throughout the day. People can perform self poojas at the place.
When Pandavas went in exile, Draupadi was extremely sad to look at the plight of her husbands. (It is well known that Draupadi was married to the five pandavas and she also accompanied them to the forests and other places in exile).
She came to Kashi and started intensely praying to Lord Surya. Lord Surya was deeply moved by her sincerity and appeared before her. He gave her one vessel and told her that the vessel would be a “never emptying vessel” inasmuch as she could go on feeding any number of guests and the vessel would never get empty.
However, she should be the last one to eat. (Even now old timers say that Guests should be fed first and household ladies should be the last to eat). Lord Surya also told Draupadi about a divine wish that Lord Shiva had given to him.
According to it, if a devotee who comes to pray to Vishveshwar in Kashi, prays to Lord Surya first, Lord Surya will have the power to remove all the sorrows which are clinging to the devotee. Lord Surya also states here that a person who sincerely prays to him at this place will never remain hungry. (Kashi Khand, Chapter 49).
The Aditya located here came to be called as Draupad Aditya.