(covers information from several alternate timelines)
The primary was named Ceti Alpha. One of these planets, Ceti Alpha V, was formerly M-class until it was devastated by the destruction wrought by Ceti Alpha VI when it exploded. The nearest starbase was Starbase 12.
Ceti Alpha V was a "habitable, although a bit savage, somewhat inhospitable" planet chosen by Captain Kirk to resettle Khan Noonien Singh and the crew of the SS Botany Bay after their attempted takeover of the USS Enterprise in 2267. (TOS: "Space Seed") Six months later, Ceti Alpha VI exploded, shifting Ceti Alpha V's orbit and rendering the latter planet incapable of supporting complex life. This was discovered when the USS Reliant visited the system in 2285. (Star Trek II: The Wrath of Khan)
In an alternate timeline, Ceti Alpha V was the refuge for the last 6,000 members of the Human species in the 2150s and 2160s, survivors of the devastating Xindi attacks on Earth and its colonies, as it was far from the Delphic Expanse. The Enterprise guided a convoy of refuges there. (ENT: "Twilight")