Asteroid 2329, Orthos, was discovered on November 19, 1976 by Hans-Emil Schuster at the European Southern Observatory. It has a period of 3 years, 266 days.
It was named for Orthos, the two-headed dog from Greek mythology. Together with his master Eurytion, this dog looked after the cattle of Geryones. One of the twelve labors of Heracles was to steal these cattle.
"Orthos" is a Greek word meaning "straight" or "correct," and that seems to be the meaning of asteroid Orthos: to be straight or to keep straight.