Its not possible directly. But you can achieve this behavior by defining the name prior to defining the array.
Here is 3 ways to do it. There can be more. But I cant recall any other way right now.
Array name is in a string
$array_name = 'awesome_array';
$$array_name = array(
'fruit'=>'apple',
'name'=>$array_name, // Name of array here
'you_are_an'=>$array_name // Name goes here too
);
Most common way
Pekka reminded me in the comments.
$awesome_array = array('fruit'=>'apple');
$awesome_array['name'] = 'awesome_array';
$awesome_array['you_are_an'] = 'awesome_array';
Dynamically collect the name
$awesome_array = array('fruit'=>'apple');
// dynamically extracting the name of last defined variable
list($name) = array_slice(array_keys(get_defined_vars()), -1 , 1);
$awesome_array['name'] = $name;
$awesome_array['you_are_an'] = $name;