SolCore

SolCore was the original name for the central human government in the Halo universe, rather than the UEG and UNSC. By the time it encountered the Covenant, it had colonized seven worlds and discovered four "lost colonies" of humans living on the alien planets.

The word Sol most likely is a reference to the Solar System or the system's medium sized star, Sol. Core most likely means that it is the core government of the Sol System and all its colonies.