Display Name not updating properly through civicrm_contact_add

If I have a contact called John X Smith then REMOVE the middle name by setting it blank and update it through the API, the display name does get updated and retains the existing full name.

$params = array(
'contact_id' => 123,
'contact_type' => 'Individual',
'first_name' => 'John',
'middle_name' => '',
'last_name' => 'Smith');

civicrm_contact_add($params);