PHPMailer generates PHP Warning: stream_socket_enable_crypto(): Peer certificate did not match expected

I had the same problem and I found the answer in the PHPMailer documentation.

PHP 5.6 certificate verification failure

In a change from earlier versions, PHP 5.6 verifies certificates on SSL connections. If the SSL config of the server you are connecting to is not correct, you will get an error like this:

Warning: stream_socket_enable_crypto(): SSL operation failed with code 1.
OpenSSL Error messages: error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed

The correct fix for this is to replace the invalid, misconfigured or self-signed certificate with a good one. Failing that, you can allow insecure connections via the SMTPOptions property introduced in PHPMailer 5.2.10 (it's possible to do this by subclassing the SMTP class in earlier versions), though this is not recommended:

$mail->SMTPOptions = array(
    'ssl' => array(
        'verify_peer' => false,
        'verify_peer_name' => false,
        'allow_self_signed' => true
    )
);

You can also change these settings globally in your php.ini, but that's a really bad idea; PHP 5.6 made this change for very good reasons.

Sometimes this behaviour is not quite so apparent; sometimes encryption failures may appear as the client issuing a QUIT immediately after trying to do a STARTTLS. If you see that happen, you should check the state of your certificates or verification settings.

For PHP 5.6 use the following. Adding "tls://" is the key.

$mail->Host = gethostbyname('tls://smtp.gmail.com');

See: http://php.net/manual/en/context.ssl.php

For those of you using cPanel, I tried the SMTP check code from the examples folder in PHPMailer and I got this same error:

PHP Warning: stream_socket_enable_crypto(): Peer certificate  CN=*.mail.dreamhost.com' did not match expected CN=mx1.sub4.homie.mail.dreamhost.com' in /home/ikbb/domains/dev.ikbb.com/public_html/includes/phpmailer/5.2.10/class.smtp.php

I realized that it was not an error related to PHPMailer, so I searched for similar errors related to CentOS and I found this link that shed some light: Issue sending mails through 3rd party. You have to take a look at "SMTP Restrictions" in cPanel.