On one hand, the whole point of having students have their own space is so that they are in control. But, if you post something publicly on the internet, it’s public. It can end up in the Way Back Machine, or archived in Google indefinitely. Works that are private and part of a class come under FERPA guidelines.
When I was teaching with Discourse, I tried hard to encourage students to always refer to each other by @usernames rather than their names. This would make it easier to reliably anonymize data by replacing @usernames with pseudonyms if the discussions were to be analyzed for resesarch. (Sure, that’ll never happen, but my undergrad degree was in CS).