Booster (or Super Heavy) is the current name of the first stage for the SpaceX super heavy lift vehicle. The vehicle was announced during the 2019 Dear Moon project presentation by Elon Musk and Yusaku Maezawa.
Booster is intended to be recoverable, with rapid turnaround between launches. Originally planned to return and land on the launch mound, the first version will have landing legs.(Musk reference)
References Dear Moon presentation youtube