Currently, all planets have fixed name. I heard stories about the original 
documentation mentioning the ability to rename planets, althought it never made 
it to the actual game.

Technically, this is possible. The only thing to consider is about the 
mission-related planets, such as Achilles, Centronom, Naxos, New Caroline, San 
Sterling and Zeuson. These are referenced by names in videos too. The remaining 
4 planets, Earth, Giantropolis, Edgepolis and Myridan are not referenced, 
although pose a historical reason to remain the same name.

If a rename option is added, the original name should be viewable in a tooltip.