The system absolutely records who posts what, based on the registered username. That's what provides assurance of identity. Unless an account is hacked, of course.

You can change the name that displays as author, but the system still knows the correct username. It could get confusing if people use the same display name; nothing prevents multiple people from going by "Robert", to pick a pointed example.

You can change the display name by going to MyTiki Wiki, then Preferences, where you'll find the display name called "Real name", in an absolutely breathtaking display of cluelessness (DamnTikiWiki). The only name that's real, insofar as real means "concrete" and "reliable", is the username, and the display name can be as unreal as you like. Clear as mud?

That other thing with "monitors" had to do with the ability to set up multiple accounts for testing, not special powers to adopt different names. We have a "TestUser" account and lots of people know how to log into it. And I maintain three accounts, 'robert', 'ubermoderator', and 'bob', to test various levels of access depending on group membership. But as for moderators having the power to adopt secret identities, nope.