A bit of history on how the name Guix System was finally picked for the distribution of GNU that uses GNU Guix as a package mananger and GNU Shepherd as an init-system, amongst other GNU maintained/developed technologies.
RMS has expressed concern about calling such a system "The GNU Operating System" and too possibly just "GNU Distro", really endorsing any distribution of GNU, over any other 3rd-party attempt to create and maintain a variant thereof. These are possible solutions, to this naming scheme.
The following were names suggested, listed in aproximate order from when they were mentioned: