You would have to alter the core files to achieve this.

My guess would be /include/class.email.php

Is is indeed possible (however not in invisible bcc) to add in class.mailer.php

$mime->addBCC('example@example.com');

But this results that the receiver does also see the BCC field somehow? Anyone help?

For us it a second question that the e-mail is not a fixed e-mail but depending on the department. How can I get the department ID in the class.mailer.php?

something like:

if ( $dept = "department_sales")
{$bccmail = sales_bcc@example.com ;}
elseif ( $dept = "department_support")
{$bccmail = support_bcc@example.com;}
else
{$bccmail = info_bcc@example.com;}

$mime->addBCC($bccmail);

How to get the $dept ?

You can try $ticket->getDeptName()

Just use the PHP function mail: https://www.php.net/manual/en/function.mail.php. This has a Bcc function.
$headers[] = 'Bcc: birthdaycheck@example.com';

To get the right department and send to the bcc of the thatI used:

$department_loc = $this->getFromAddress($options) ;

if ( (strpos($department_loc, 'service') !== false) )
{$deptmail_bcc = "service_bcc@company.com" ; }
elseif ( (strpos($department_loc, 'sales') !== false) )
{$deptmail_bcc = "sales_bcc@company.com" ; }
elseif ( (strpos($department_loc, 'info') !== false) )
{$deptmail_bcc = "info_bcc@company.com" ; }
..
..
..

    else
            {$deptmail_bcc = "unkown@company.com" ; }

$mime->addBcc($deptmail);