Dakshayani is one among the numerous names of Mother Goddess Shakti. Goddess Sati is known as Dakshayani. She is known by the name because she was the daughter of Daksha Prajapati.
Goddess Sati had married Shiva against the wishes of her father Daksha.
Daksha once planned to perform an important yajna. He invited everybody but Shiva and Sati was not invited.
Sati considered this as an insult and she took permission from Shiva and went to the place of yajna. Sati was insulted by Daksha.
Sati was filled with anger and sorrow. She declared that she cannot remain in this body which is the result of her father Daksha. She announced that she can longer bear to be called Dakshayani. She then self immolated.
Dakshayani is Goddess Sati. She is dark in color. She is daughter, devoted wife and fierce Kali.