Eumolpus was a son of Poseidon and Chione (or Dysaules and Baubo). It means 'sweetly singing', from eu-, 'good' and molpe, 'song', 'singing'. The name suggests some religious or mystical ceremony, and in fact Eumolpus was associated with the founding of the Eleusinian Mysteries.
Lucian tells us that Eumolpus was a title adopted by the chief priest of the Eleusinian Mysteries when in office, since he was not supposed to use his own name at this time.