Depending on how many users/new user signups you have and how many moderators/admins, this could quickly become unmanageable.
There is also the potential for abuse by other users.
Let’s say user X happens not to like user Y’s profile name and reports it but actually there is nothing wrong with the name.
The moderators will spend more time dealing with these flags rather than staying focused on more problematic ones.
Theoretically, if there was something wrong with the user profile it could be reported with a flag, like Something Else, if they post something.
There might be other ways to achieve what you want like Watched Words for user names, though I suspect there would be limitations to that approach.
Profile pictures/avatars, not sure how that could be dealt with.