Stapledon Center was part of a Federation colony in the Wolf 359 system. It was one of 33 extrasolar colonies in 20 different star systems established by warp-capable craft between 2061 and 2079. The colony was known for its molecular computer farms.
In the early 2100s, Zefram Cochrane left Alpha Centauri, supposedly heading for Stapledon Center, and disappeared. (TNG novel: Federation)
The other colony in the same system was Yogyakarta Baru. (Star Trek: Shadowstar Station)
Speculation[]
The colony may have been named for the author Olaf Stapledon. In his 1937 novel Star Maker, one of the extrasolar civilizations he described live on the terminator zone of a tidally-locked planet orbiting a red dwarf.