Itylus was the son of Zethus and Aedon who was killed by his mother by mistake (see Aedon for the story). Without stretching the credibility too far, we can make his name mean 'little nightingale'. We know that his mother's name means 'nightingale' and if we take his name as a diminutive of Itys (which see) it could refer to the song of a young nightingale and thus to the bird itself.
Maybe little Itylus had a good singing voice. Whatever the case, it is significant that both Itylus and Itys suffered the same fate, for both boys were killed by their mothers. There seems little doubt that their names are linked in identity of fate, if not in actual meaning.