It happens When the "NT Authority\Authenticated Users" are added to Site's Visitors/ reader Group. If you check the user profile at the central admin it gets updated but it didn't update the site collection.
You will face this issue on Intranet site where the user has read only permission.
To fix this issue
1. Create a temp list somewhere in the site
2. Go to the list permission and Break the Inheritance
3. Add new user- search for the user-(it will show you the previous name)
4. Wait for a minute- and the user profile will get updated with new name.
5. Delete your temp list.
It worked for me.
For more info:technet