Ensure user's nickname and display name are unique and not a display name or nick name or user name of someone else
Validate Profile Credentials and Names
In a WordPress site users have multiple names in their profile, the user login, display name and nick name. In a multi-user site, there is often a need to keep them unique. You need to allow users have only credible names, such that,
Credible Names is a easy plugin to help you with that.