So why the rebrand?

Originally IT: Underswap? stood for "Is This Underswap?" though we felt like this name did not fit for a variety of reasons, with the main reason being that it could be misread and interpreted differently because It is an actual word.

Why stasis then?

Stasis is a state of preservation. This fits the idea of the game because life underground is being preserved. But also because most instances of an alternate world, the underground is in constant need of hunting and retrieving souls. This preserves the underground for the player to solve, or end all the suffering underground.