DuckDuckGo is a great brand, it would be great if we could expand to more than just search (email, docs, etc.) One idea I had was a URL shortener: I know there are millions of them but that just means they're not too difficult to make.
Many URL shorteners require you to sign in/track you/are very complicated, meaning that DuckDuckGo could succeed here. DuckDuckURLShortener can be simple and anonymous - it doesn't track people who shorten URLs or visit those shortened URLs.
I haven't found any untaken domain names that would work. ddg.us (DuckDuckGo URL Shortener) is a good one (short and memorable), but it's taken by a domain squatter. Of course, though, we can worry about the domain name later.