For such task, you should really be using PHP's DateTime class. Please ignore all of the answers advising you to use date() or date_set_time_zone, it's simply bad and outdated.
I'll use pseudocode to demonstrate, so try to adjust the code to suit your needs.
Assuming that variable $tz contains string name of a valid time zone and variable $timestamp contains the timestamp you wish to format according to time zone, the code would look like this:
$tz = 'Europe/London';
$timestamp = time();
$dt = new DateTime("now", new DateTimeZone($tz)); //first argument "must" be a string
$dt->setTimestamp($timestamp); //adjust the object to correct timestamp
echo $dt->format('d.m.Y, H:i:s');
DateTime class is powerful, and to grasp all of its capabilities - you should devote some of your time reading about it at php.net. To answer your question fully - yes, you can adjust the time zone parameter dynamically (on each iteration while reading from db, you can create a new DateTimeZone() object).
You can replace database value in date_default_timezone_set function,
date_default_timezone_set(SOME_PHP_VARIABLE);
but just needs to take care of exact values relevant to the timezones.
If you use Team EJ's answer, using T in the format string for DateTime will display a three-letter abbreviation, but you can get the long name of the timezone like this:
I have tried the answers based on the DateTime class. While they are working, I found a much simpler solution that makes a DateTime object timezone aware at the time of creation.
$dt = new DateTime("now", new DateTimeZone('Asia/Jakarta'));
echo $dt->format("Y-m-d H:i:s");
This returns the current local time in Jakarta, Indonesia.