Drupal 8: How to get the ['third_party_settings'] of an image field inside hook_preprocess_image_formatter(&$variables)
Although this is pretty specific, it may help someone else with a similar problem.

The answer is in getFieldDefinition() object of $variables['item']. 

In order to acquire the field name of an image object from within HOOK_preprocess_image_formatter(&amp;$variables) which is a variation of HOOK_preprocess_HOOK(), you would use: 

$field_name = $variables['item']-&gt;getFieldDefinition()-&gt;getName();

Used within the context of a module file it would look something like the following:

/**
 * Implements hook_preprocess_HOOK()
 * This allows us to pass attributes to the image_formatter template.
 */
 function MY_MODULE_preprocess_image_formatter(&amp;$variables) {
   // Get the field name
   $field_name = $variables['item']-&gt;getFieldDefinition()-&gt;getName();
 }