I agree with anonymity being better in general, but I don't think that would achieve much towards it. Take a team like Cali - sure, they could swap players around, but that would require one of the best gunboat players in the world not playing gunboat, one of the best public press players not playing public press, and two of the best FP players being moved out of their comfort zone too. The most they could do without ruining their team is swap around the two FP players, and even then it's not hard to figure out who is who.
Even when you don't know who the player is, there are things you pick up on automatically that give hints. This player is using British English -> they're probably on team GB, English is clearly not this player's first language -> they're probably on a non-English-speaking team, this player doesn't seem all that good -> they're likely on a low-GR team and so on. You don't even need to look for these, it's incredibly hard to miss them.
When you know who the players are you then there's the additional element of knowing how some of them talk. Certain players have phrases they use a lot, some players don't capitalise or punctuate, some players use smileys, etc etc. Again, if you've played with these players a bit before it's hard to miss. Balki's idea might help this section a little.
If you really want anonymity, teams should be submitted privately to the TD at the start of the tournament, or players should just sign up with their location/nationality and the TD should arrange the teams, then the team names could be released but not the players themselves. This would take the metagaming aspect out of the first round, at least.