The Orion system was an inhabited star system in the Orion sector of the Alpha Quadrant. The primary was named Orion. (TOS: "What Are Little Girls Made Of?": TAS: "Yesteryear"; Star Trek VI: The Undiscovered Country, production art; VOY: "Good Shepherd")
According to The Worlds of the Federation (page 36), the Rigel system and the Orion system are one and the same. The eight planet in the system is the planet Orion, the homeworld of the Orion species. According to Star Trek: Star Charts (page 36), the Orion system was Pi 3 Orionis, a trinary star system located in the Beta Quadrant.