I've gone through and I think I've fixed all the problems. Here are the relevant #changelog entries.
- CHANGE: Tweaked the wording of 'Changed display name' activity log entries to be more clear.
- BUGFIX: If someone had changed their display name for a particular subscription, and then changed their display name through their overall profile, an activity log was generated incorrectly saying that the modified display name had been changed, even though it had not.
- NEW: There is a new activity log entry type, 'Moderator changed display name'.
- BUGFIX: Display name activity log records were generated even when the display name wasn't changed when editing a member.
Please let me know if you see anything else.