I'm in the camp that regardless of the name we'll get just as many things marked complete that do not seem to be so to an external observer. Personally I have no problem with some people falsely declaring complete our success when they shouldn't. I model off naniwrimo, where you can quite simple submit fifty thousand "a"s and get marked as a successful novel.
That all said, better name may reduce the"run aways" at the end. I like Darren's names: success and unfinished. As Darren says, you don't finish the challenge if you don't have a finished game!