I believe it is important for the mods to know if a single user is making a ridiculous number of reports, or spamming reporting of a single user's posts.
However, if it is possible for each user to be assigned a randomized code (only showing for report flags), which the mods will not be able to use to identify any specific user, I believe this would solve both problems.
I am in favor of setting a code to allow mods to identify how many reports are being generated by a single person.
I am not in favor of attaching a specific username to each flag.
If I had to choose between "anonymous flagging" and "identified flagging", I would choose "anonymous flagging" as the lesser of two evils.
However I am also very much in favor of setting an anonymous code to allow mods to identify duplicate reports (flags) and spamming.