SharePoint user - when there are changes in AD

When some user data change in AD (e.g. last name) this change in most cases is not properly synchronized to SharePoint site collection.
The following Power Shell commands may help:

$user = get-spuser -Identity domain\username -Web http://server:port
Set-SPuser -Identity $user -SyncFromAD

Sadly it doesn't help in case an account name in AD has been changed. Then we have an orphaned user situation and the solution is to delete the account in SharePoint.
If it's only one site collection with couple of users, the quick way is to do it manually via Site collection - go to this page: http://sitecollection/_catalogs/users/simple.aspx