Can the moderators see who is flagging a particular post? Does it come anonymously like we see in "Close Votes" review? Or the name of the person who is flagging is shown to them?
Moderators can see who is flagging a post.
Close votes are not entirely anonymous either, when 5 votes are cast (or the first moderator vote), the users who voted to close the question are visible to all, and named in the close notice. They only retain anonymity until that threshold is reached.
I think this is mostly good, you should be willing to be seen to vote to close a post, or to flag a post too. The ability to hide behind anonymity could be a cover for mean behavior. People who flag or close should do it for the benefit of the site community, and therefore should be happy to be seen. Luckily this is fairly typical of the regular users here.