the "zanshin" you're referring to is written 残心, and as you said, has to do with the practitioner's awareness.
Hakumen's drive name, however, is written 斬神, which literally means "slash-god", but is probably better translated as "god slash".
in japanese, homonyms abound! always check the kanji, if you can, before assuming something like that.
edit/p.s.: if you can't see kanji on your computer, then you won't see what i wrote, so you'll just have to believe me when i say they're written differently and are thus merely homonyms.