If you want to do it lawfully, no, it will not be completely anonymous. The moment you change it into fiat, they will have your credentials. The only way I can think of is that you find a group of people who are willing to buy it, and you meetup and exchange it for cash.
Not completely anonymous in the sense that you are not sitting behind the screen, unknown to everyone. Like what he said^, just spend it online for completely anonymity.
Even if you try to buy items with Bitcoin to resell, you may be questioned on how you got the goods and so.