Recently I got an issue in my SharePoint 2013 production environment. One of the user display name not showing properly. Instead of his name, it is showing one of the employee who left the organization. By checking the user details in AD we got the details. AD team updated two emails for one user. One is his own email and other email is one of the employee who left the company. We tracked the issue and updated the profile AD and ran User Profile Sync. Everything worked well till now.
But user still having the issue in one site, his display name not showing correctly. Instead of his name, it is showing employee who left the organization. We are seeing this issue only for one site collection. Tried different approaches like deleting user permissions in the site through UI and using PowerShell commands. Nothing worked.
After Googling the issue, we got the resolution. We are seeing that issue due caching in SharePoint site collection. When I remove and add the data in SharePoint site group, SharePoint site collection user details from all users located in <Site URL>/_layouts/people.aspx?MembershipGroupId=0
To fix the issue, we need to remove the user from all users list and read it to the list. But before that we need to check all the user permissions in the site (including all the groups and individual permissions) and need to re add all the places.
Hope this helps.