Hello Yoann,
Yes, this is possible. Here's a sample:
$oldValue = $Context.TargetObject.Get("sAMAccountName")
$newValue = $Context.GetModifiedPropertyValue("sAMAccountName")
Please, keep in mind that such a script should be run before updating a user account. After you update the account, both the $oldValue and the $newValue will contain the current username.