In application/views/event you have different files for the different calendar views i.e.
In viewweek5days.php around line 320
Try replacing
$objType = 'task';
$subject = clean($event->getTitle());
$divtype = '<i>' . $tip_title . '</i> - ';
with
$objType = 'task';
$subject = clean($event->getAssignedToName()) . " - " . clean($event->getTitle());
$divtype = '<i>' . $tip_title . '</i> - ';