For example, if it's a popular thread and a staff member edits something inappropriate out in the OP, a member would see Last edited by Brogan: 1 minute ago, as you stated, but if the OP then later edits to update information, they'll see Last edited: 23 minutes ago.
I feel like some members, especially new members, would find that confusing if they saw it go from Last edited to Last edited by [Staff Member] or vice-versa -- or even some back and forth action.
Ah, okay. Now I get it. And then when the author edits it, it'll just say "Last edited." I thought you were using "a moderator" as a placeholder for whatever staff member's name like when I had [Staff Member].
I think I'll change my suggestion, then, to re-phrasing "moderator" to "staff member" since there are also administrators.
While administrators may not be directly moderators, though, they can still edit posts just the same, so this is where I think having "staff member" instead of "moderator" would be better, since staff member can be applied to any staff and not just one user group, such as Administrators, Super Moderators and Moderators.
An alternative option, I guess, could be that if a moderator edits your post, it says "moderator," but if an administrator edits your post, it says "administrator."
Not in my forums, no. The initial administrator installed by the software does since it can be assumed that the initial account will be the only staff member at first, so inherently needs them. The verbiage of "moderator" implies that someone with moderation capabilities, since not all staff members will have them unlike in other software.
I ascribe to the whole assign moderator permissions via the moderator group + individual permissions when creating the user as a moderator. The individual permissions elevate certain users (me) to have more permissions such as hard delete permissions.
I agree with Amaury. Especially on large boards a moderator can be one of 10-20 people. So if just the user edited their post, it can say 'last edited', but if the moderator edited it, it should say 'last edited by moderator (Name)', for easy identification.
The only reason which I can think of, why providing the moderator's name can be useful, is that you give the user the ability to discuss the edit with the specific moderator. However on many forums moderator decisions shall not be discussed and it can be helpful not to mention the name to reach this goal.
To make all people happy, maybe providing the name should be optional? I always like to have options!