Orthus

Orthus or Orthrus was a two-headed dog, the offspring of Typhon and Echidna. It guarded Geryon's cattle and was killed by Heracles. If we take the spelling Orthus, then we may have orthos, 'straight', 'true' as the meaning behind the name.

If we prefer Orthrus, we may have orthros, 'dawn', 'early morning' as the root, with the general sense being 'early'. Both interpretations would suit a dog that looked after cattle, since it would have to be 'true' and work in the early morning. In his Theogony, Hesiod makes Orthus and Cerberus brothers.