Serpents of Lord Shiva:

The snakes coiled at different places of Lord Shiva's body have names.

The serpents coiled at His ears are named Padma and Pingala.
The serpents coiled at His armlets are named Kambala and Dhananjaya.
The serpents at right and left wrists are named asvatara and taksaka.
The serpent at his waist is called Nila. (Vamana Purana)

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The snake swirling around his waist is kundalini, the Shakti or divine force thought to reside within everything.