yeah, I was for naming hit points Stamina.
Though in original D&D hit points were an abstraction and not actual life, that was altered in later editions as I recall. Hit Points are better than Health Points, but they do carry that feel.
I don’t think Damage is a bad term necessarily, but renaming Hit Points to Stamina (or Endurance), and Lethal Damage could just remain the same honestly.
When players in my games are “hit”, I do my best to describe it as exerting themselves to just barely miss the blow. Only describing it as a hard it if lethal damage is applied. Like reddevil said, this can be easier “said then done” though, coming from other games.
Another term instead of Stamina could be Stress… though that usually works in counting up instead of counting down.