Let me tell you from my 20 years of experience on the internet..... NO! DON'T!
Transparency is normally a good thing, but some things can put better behind closed doors. A good community logs stuff anyway and admins (and quite often fellow moderators) can easily see these logs and take proper action.
I've seen entire communities turn against one moderator, who was right all along by the way, and I've even seen one community die due to a situation like that.
If a moderator is really in error (moderators are humans, after all), the administration should when things are properly logged find out who that was anyway. Too much visibility will undermine a moderator's authority, and the entire functioning of the community in the process. Actions against such a moderator, even just a notice, or a warning or even dismissing a moderator should then happen backstage. If a moderator wants to reveal themselves, then that's their choice, and in some situations they should. On some big sites I moderated I've done on countless occasions, and a good moderators does not back out from that if such situations arise. In the general sense no, and for that reason I will also never reveal the name of a moderator who took a certain action, when you complain about my fellow moderators.
Most sites keep that information secret of good reasons.