You can use below powershell command to change sharepoint user display name.
Set-SPuser -identity "User name" -DisplayName "Display Name" -web Web url
Note: for AD user username would be like domain name\username. For FBA user it would be like i:0#.f|providername|username (You can get the exact username from My Settings page.
In case you get access denied while changing the display name, run powershell as administrator/Farm admin. You can get this option by pressing shift key then right click on Sharepoint powershell management console icon.
