There are numerous stories regarding how Mother Goddess Shakti came to be called Goddess Durga. One such story states that Goddess got the name Durga after annihilating the demon Durgama. Legend has it Asura Durgama was born in the lineage of Hiranyakashipu and Hiranyaksha.
Durgama soon realized that the reason for the invincibility of Devas and Saints is Vedas. So he did intense penance with aim to steal Vedas. Brahma could no longer ignore the intense Tapas of Durgamma and appeared before him.
The demon asked Brahma for the total control of Vedas and also that he will not be killed by gods, men, gandharvas, yakshas, nagas or animals. Brahma granted the boon.
Soon Durgama took control over the Vedas and hid it in a cave in the Himalayas. Saints forgot all the mantras and Devas started to lose their powers. Soon Durgama and his forces overpowered heaven.
With Vedas gone there was no havan or japa or yajna as a result there was total chaos in all the worlds.
All saints assembled and propitiated Mother Goddess Shakti to find a solution.
Mother Goddess Shakti appeared in the form of Jagadamba and promised to find a solution.
Soon a battle ensued between Goddess Shakti and Durgama. The demon had become very powerful and the battle continued for several days and Goddess Shakti appeared in several forms Kalika, Tarani, Bagla, Matangil, Chinamasta, Tulja, Kamakshti, Bhairavi etc.
The demon could not withstand the combined assault of the various forms Shakti. He was overpowered.
Vedas were restored.
Goddess Shakti earned the name Durga after killing the demon Durgama.