If you want to get a different kind of anonymous, what you could do is have everyone in single player brackets to start for the first 6 days, each named after them so that others could still spy on them. And then once the last 24 hours hits, suddenly throw everyone into proper brackets so that for the entire week, you had no idea what people were planning on doing, what they were going for or what the bracket will look like.

There would be a last minute rush to get cards, form alliances and really just do everything. People could still save visits for a last minute switch. Or what one could do is for the first 6 days, have everyone in the same bracket so that they can still attack each other but then have it break up on the seventh day. That would be hectic like all hell.