What are the design goals, guiding principles or reasons behind what you're working on? Without knowing the character of the project, the names are going to be fairly generic. Of course, if you're working on yet another web desktop, you could call it "yawd".
"clOS" might be confused with the Common LISP Object System, at least by search engines.
If you want to go with a spider theme, consider "ArachnOS" and "AraneOS". If you're working on a web desktop rather than a
web operating system, you could use "cloWD" or "LeWD" (think French).
There are a number of great names that may not be particularly relevant. "NachOS" and "TacOS" for the snackers. "KazoOS" and "BanjOS" for the musical. Along the same line is "BongOS", but that's too easily misconstrued. Finally, "HobOS" and "WinOS" are always relevant, though the latter might be taken to refer to a certain product from Redmond (and not just because
alcohol is involved).