Chordates derive their name from one of their synapomorphies, or derived features indicating their common ancestry. This is the notochord, a semi-flexible rod running along the length of the animal.In those chordates which lack bone, muscles work against the notochord to move the animal.hordates derive their name from one of their synapomorphies, or derived features indicating their common ancestry. This is the notochord, a semi-flexible rod running along the length of the animal.