I wanted to configure the “From” email address that WordPress uses when emailing password resets. The way to do this is with a WordPress hook, specifically a filter hook in this case. So, in wp-config.php I added the following code:

add_filter( 'wp_mail_from', 'pcblog_mail_from' );
add_filter( 'wp_mail_from_name', 'pcblog_mail_from_name' );

function pcblog_mail_from() {
  return 'pcblog@progclub.org';
}
function pcblog_mail_from_name() {
  return 'ProgClub blog';
}