I have written out a Dyson Sphere world with four cities that surround four colossal oceans (each >16000000x the volume of jupiter). I've worked on the flora, fauna, government, pseudo-gravity and so many other things, but I don't have a name for the Sphere itself.
It's year of completion is around 3450. It's construction began after the destruction of the earth due to being knocked out of orbit during WW4 ~2350 which lasted a few weeks (WW3 was relatively uneventful). Most of human history was lost, though several Exabytes of data were preserved containing 3D scans of artifacts and some information concerning language and culture. This data led to the oceans being named and shaped after the Greek letters Theta ϴ, Omicron O, Phi φ and Omega Ω. The cities are named after the ocean they surround.
What should the sphere as a whole structure be called? Ancient references are good but astral reference is also cool. Parts of the world refer to history, the stars, mythology. For example, two transportation systems are named after the 4200 pole stars, Cephean (north) and Chameon (south).