Update DisplayName in sharepoint

Normally, If you configure user profile correctly it should update user display name. I have situation where user is not in user profile ,but I need to update display name. here how I do it using power shell

$user = Get-SPUser "I|0#.claim:username" -web http://servername
$user - to display the name
$user.DisplayName = "New Display Name"
$user.Update()
$user - to display the updated name