Assuming you're using a Linux server...
From the manual entry for http://php.net/manual/en/ref.mail.php:
sendmail_from string
Which "From:" mail address should be used in mail sent from PHP under Windows.
The earliest User Comment (at the bottom of the page) has some more information.
If you use the optional "additional_headers" parameter for mail() you can override the defaults, e.g.,
$header = 'From: Tester <tester@example.com>' . "\r\n";