The difference between how comments render to pages vs. groups is due to a Facebook API change and how permissions on Facebook work for groups vs public pages. This is not a bug but rather a Facebook API permissions expectation.
In April of 2018, Facebook changed the way the groups API worked. (You can read more about these changes in the link below on Facebook’s website), and specifically this change prevented APIs from seeing the names of users making comments. This was a breaking change, meaning there was no solution around it for service providers and it impacts all service providers.
Since April, Facebook has slowly introduced some beta group API features to enhance the groups experience as it relates to APIs and reading user names on things like comments. However, this new method does require users to opt into letting the app see their name / each user needs to add the app to its profile. If a user is not specifically letting the app see it’s profile, comments are anonymous.
As you can imagine, it is not very likely that all users in a group will be following these steps for use cases like live video streaming applications, as group users tend to be passive viewers and not broadcasters that need the app and thus will accept the permission.
In terms of improving the groups experience within ClearCaster, we are keeping a pulse on how Facebook evolves this permission. But as it stands right now, privacy settings for users in groups is different than pages, and thus it should be expected that group members are anonymous.
For more info on the breaking changes Facebook made for privacy reasons, see here: https://developers.facebook.com/docs/graph-api/changelog/breaking-changes/#groups-4-4).