According to Hindu mythology, Jalandhar, the king of demons had terrorized the gods with his power and whenever the devas tried to defeat him his power would increase as his devoted wife Vrinda would pray to Lord Vishnu for her husband's victory. The gods then went to Lord Vishnu for seeking help and requested him to vow Vrinda, as her husband could only be defeated if his beloved wife would commit adultery outside her marriage.
Vishnu used his charm to tempt Vrinda but her love and devotion for her husband didn't shake her morality. Having no other escape, Lord Vishnu then disguised as Jalandhar and violated Vrinda’s chastity. Jalandhar was eventually killed by Shiva, upon realizing that Jalandhar had died, Vrinda cursed Lord Vishnu that he will turn into a stone and will scatter everywhere in the territory of king Jalandhar. Hence, the place got its name Harsil.
While the other folklore tells that the two rivers, Jalandhari and Bhagirathi always fought with each other to prove their metal. The fighting caused turbulence and terror in the areas nearby, the mortals then prayed to Lord Vishnu for resolving the issue. Vishnu listened to their prayers and transformed into a 'Sila' or stone. He placed himself in the midst of the confluence of Jalandhari and Bhagirathi rivers. Therefore, the place was named Harshil which literally suggests Lord Vishnu in the form of a rock.