As a moderator, you have the following tools available, in no particular order:
1. you can freeze the room - only moderators can chat then
2. you can kick individuals
3. you can see the edit history of all posts
4. you can use some tools which can help identify whether a person is also actually someone else
5. you can see the suspention history of a user
6. you can see any previously flagged chat messages (but not who flagged them)
7. you can suspend users for pretty much any length of time (up to a year is easu, a century takes more effort)