Omega system

From Memory Alpha, the free Star Trek reference

The Omega system is the solar system that includes Holberg 917G, a planet purchased by Mr. Brack in 2239.

The USS Enterprise visited Holberg in 2269, Stardate 5843.7, in order to obtain the ryetalyn that could combat the deadly Rigelian fever threatening its crew. "I have monitored your ship since it entered this system," Flint told the landing party. (TOS: "Requiem for Methuselah")

"Omega" is most likely short for a real star with an "Omega" in its name. It is not likely to be the same primary around which orbits Omega IV, the world seen in TOS: "The Omega Glory". The use of such short names is common in the 23rd century, for example the Alpha system apparently indicated in TOS: "Court Martial".