Hi Felix,
Another participant actually asked the same question in a private email so it's probably worth telling the whole group.
Yes, the paper authors should be anonymised, but no, you shouldn't anonymise team names or other identifying information. While this will make it relatively easy to identify specific authors, all shared task papers will get published anyway (unless they are low quality) and so reviewer biases don't really matter. Shared task paper "reviews" are ultimately more about proofreading and feedback, and so lack of anonymity won't be held against you.
We only ask for author anonymisation because the main BEA organisers told us it would make it easier for them to handle the review process if everything is submitted in the same way.
Hope that helps,
Chris