This thread made me think of having anonymous games too. I think it would need to be built in though as otherwise you'd be able to look at people's partial emails and profiles and see who they were and get an idea of how experienced they were. It would also allow blind chat where you can't tell even which color player is saying what so it would allow for all sorts of trickery. Not sure how fun it would be compared to a normal game, but would definitely make things interesting.
I welcome the challenge of someone who thinks they can impersonate me and trick someone else into doing something they wouldn't otherwise do.
Of course it could run into this issue: http://penny-arcade.com/comic/2004/3/19/
Maybe once the game is over defog the chat color & names so you can see who said each line.