Poseidon is the name of an Ancient Greek sea-god, later known as Neptune by the Ancient Romans.
In the Mythos[]
Father Neptune once appeared to Thomas Olney, holding a trident and accompanied by scores of tritons and nereids, as well as the primal god Nodens. (HPL: "The Strange High House in the Mist")
According to David Parker, Neptune, Dagon and Cthulhu are all different names for the same entity. (EXP: "Dagon's Bell").
In the expanded Cthulhu Mythos, Poseidon is a powerful extragalactic entity, awed by 'Ymnar. It battled against the Elder God Paighon.