Shankari is one among the numerous names of Narmada River. When she is referred as Shankari, she is the daughter of Shiva. This story is mentioned in the Skanda Purana.
Once, Shiva and Goddess Parvati performed intense meditation and austerities atop the mountain Rikshasaila for the welfare of humanity. The sweat that formed on Shiva’s body flowed down the mountain and took the form a beautiful woman.
She was liked by the Devas and Sages.
Shiva named her Narmada, the giver of delight.
As Narmada sprung from the body of Shiva, she is also referred as Shankari, daughter of Shiva.
Please note that Shankari is also one among the numerous names of Goddess Shakti. In this context, the meaning of Shankri is ‘one who is loved by Shiva.’