Users impersonating other users using "display name"

I’ve got a very large WordPress install and there tends to be very heated discussion on the articles.

Users have to have a subscriber account to comment and in the comments, we display who they are using the “Display Name” field. Recently users have been signing up for new accounts and changing their display name to the same thing as another user in order to impersonate them.

Is there any way to enforce unique display names in user profiles?

Any help would be appreciated.