The 'best' way to do this would be to set a property on a view object once the update is successful. You can then access this property in the view and inform the user accordingly.
Having said that it would be possible to trigger an alert from the controller code by doing something like this -
public ActionResult ActionName(PostBackData postbackdata)
{
//your DB code
return new JavascriptResult { Script = "alert('Successfully registered');" };
}
You can find further info in this question - How to display "Message box" using MVC3 controller