Milotics name may be a combination of melodic + milos (like the aphrodite of milos that represents beauty and like Milotic, possesses no arms)
Milotic also have a wide range of healing and defensive moves, so its name may also be related with mitosis (Healing process of the body, regeneration of cells)
Gyarados's name may be derived from a combination of gyakusatsu massacre/slaughter, and gyakkyō, hardship/adversity. Both words relate to the creature's violent nature and the hardship it experienced before evolving. The DOS may just indicate that it's the second in its evolutionary line.