Is system/planet/etc naming based on first to discover or first to upload?

For PC, yes, if you don't upload your findings, someone else can come and take credit for your discoveries.

I can speak from experience. In the new BEYOND update, traveling to the Anomaly allows other players to teleport to your base up using the on-ship teleporter system. One time, after a visit to Nada and Polo, I saw another player had come to visit my base. At first I thought this was kinda cool, but then I realized the player uploaded my home planet for his own gain AND renamed it after himself. He then started doing the same for all the animals he could find on the planet. (I don't usually upload discoveries because I don't need the nanites and encountering another player during normal gameplay is typically impossible.) Heck, he even started building a base of his own right next to mine!!! So rude. Obviously I was upset, so I packed up my base and moved to a different system.