Neelakantha is the name given to Shiva after he holds deadly poison in his throat.
During the churning of the ocean of milk, a lethal poison called halahala emerges before the gods and asuras obtain the treasures they seek. The poison threatens all creation. Shiva drinks it to prevent catastrophe, but Parvati restrains it at his throat so it does not pass into his body.
The poison stains his throat blue, producing the epithet Neelakantha, commonly translated as “blue-throated.” The story explains a visual feature frequently associated with Shiva in Hindu art and devotional literature.
Neelakantha is an epithet rather than Shiva’s personal birth name. Other famous titles have different meanings: Pashupati means lord of animals, Mahadeva means great god, and Nataraja identifies Shiva as lord of the cosmic dance.