Activity - Send a Copy Email
It used to be the logged in user but I guess some people didn't want that and it was changed in https://issues.civicrm.org/jira/browse/CRM-20308

So it now uses the order listed there:


The Reported by Contact's email address
System Default From Address
Default Organization Contact email address
Logged in user


Personally I think logged in user makes more sense, and you could have privacy and also antispam problems with the Reported By address if it's not the org's domain.

It looks like there was a setting added to allow the old behavior, but it's not clear how it's supposed to work. It looks like to prevent using the Reported By contact you would uncheck the setting "Allow Mail to be sent from logged in contact's email address" found at Administer->system settings->Outbound Email, except then it would always return the system/org-wide email address.
https://github.com/civicrm/civicrm-core/commit/4c981f371a6602cdfcda525895e0d0c40e9294d9#diff-be8afcc653a18926aabd2b40be8469f9

If you want a quick hack, try changing line 1407 in CRM/Case/BAO/Case.php from:

$receiptFrom = self::getReceiptFrom($activityId);


to

list($receiptUserName, $receiptUserEmail) = CRM_Contact_BAO_Contact_Location::getEmailDetails($userID);
$receiptFrom = "$receiptUserName &lt;$receiptUserEmail&gt;";