This was driving me nuts so I'm adding a note here.
Took a while to get the simple time zone abbreviation for a given time zone. If you have the name just do this:
<?php
$dateTime = new DateTime();
$dateTime->setTimeZone(new DateTimeZone('America/Los_Angeles'));
return $dateTime->format('T');
?>
Will return PST
[red.: Or PDT is the current date/time is during Daylight Savings Time]