The Modlog is (or should be, in theory) accessible on any Lemmy/Kbin instance. However, it is on an instance by instance basis whether the Modlog shows full information for each moderator action. Like you said, some instances will only show “mod” but others will provide the names.
To be honest, I haven’t been looking at the Fediverse a whole lot lately, so I can’t recommend which ones are the best and most transparent. At one point in time, the Lemmy.world Modlog did provide full info but it seems that they have changed that in recent months.