Pyramus was the well-known lover of Thisbe. Their story was retold by Shakespeare ('the most lamentable comedy, and most cruel death of Pyramus and Thisbe') in A Midsummer Night's Dream. Since the story originated in ancient Babylon - as Ovid admits, when he tells it in his Metamorphoses - the name of Pyramus may well not be Greek.
It may somehow be connected with 'pyramid', an Egyptian word, or with pyramous, a Greek word for a kind of cake given as a prize to a person who kept awake the longest in a night watch. (This up to a point ties in with the long night whisperings through a chink in the wall that Pyramus and Thisbe had to resort to since their families would not allow them to marry.)