The company name was conceived to fill the gap left by all the no good software products available on the market, none of which fully meet customer needs.
To highlight the subtle message the name is trying to convey is that people complain of having no good software to do X or to do Y. Paradoxically, the messaging is that No Good Software builds software which does in fact do X or Y and values users highest.
Another pun being toyed with was the use of the homonym, "know" i.e. to "Know" Good Software. Wanted to put that out there in case it lead to some ideas but hopefully it won't be misleading
Simplicity and cleanliness are key.
Not necessary to inlcude the "Inc" in the logo.
In general, I'd prefer to have an icon appear in the logo to help in the sense of identity.
Another suggestion, coming to mind is that of "No Good Software" to the rescue of software so perhaps something conveying this e.g. red cross package, parachute. Something this obvious might be a little tacky but a subtler message may work better.