Phorcys was an ancient sea god, one of the original 'Old Men of the Sea'. He was the son of Pontus (or Nereus) and Gaia, and the father of a number of monsters by Ceto, including the Graiae, the Gorgons, Echidna, and so on. His name may well link up with the sea monster called an 'ore' (see Orcus) or else be a 'brutish' name related to Latin porcus, 'pig'.
On the other hand his name could be associated with phero, 'to bear', 'carry', this being a reference to the motion or current of the sea. But this hardly seems unpleasant enough for one who fathered such a horrific clutch of monsters. (Among his other offspring, according to some writers, was Scylla.)