The Garhwal Himalaya holds the headwaters of the Ganga, and with them one of Hinduism's oldest legends. King Bhagirath, it is told, undertook a penance of extraordinary severity to bring the celestial river Ganga down to earth, so that the ashes of his ancestors, the sons of Sagara, might be sanctified and their souls released.
Ganga agreed to descend — but her fall from heaven would have shattered the earth. Lord Shiva therefore received her in his matted locks, taming the torrent and releasing her in gentle streams. The place where her waters emerge from the ice — the snout of the Gangotri Glacier at Gaumukh ("the cow's mouth") — is revered as that meeting point, and the river here is named the Bhagirathi after the king whose devotion summoned her.
At Gangotri a temple marks where Ganga is worshipped as a goddess; by tradition Bhagirath meditated on a rock nearby. Only downstream, at Devprayag, does the Bhagirathi join the Alaknanda to take the name Ganga.
Sources: en.wikipedia.org, britannica.com. Retold from documented tradition.