Is there a way to prevent users from signing up with certain words in their usernames so they can’t imitate our moderators or fake an official account?
Hello, welcome to Meta! 
I believe, the reserved usernames setting is what you’re looking for:
where can I find this setting?
That looks like the mod view, are you sure you’re admin?
You need to be an administrator to change the site settings.
This is the moderator’s view you’re looking at.