PHP: Update global reference variabele inside function scrope

I’m trying to change a global value that is currently a reference to another value. My current implementation doesn’t work:

$anna = array('Name' => "Anna");
$bella = array('Name' => "Bella");
$girl = &$anna;

function change(){
    global $girl, $bella;
    $girl = &$bella;
    // $girl['Name'] is now 'Bella'
    output_girl(); // This still outputs 'Anna'
}

function output_girl(){
    global $girl;
    echo $girl['Name'];
}

change();

// What do we want to see?
echo $anna['Name']; // Should still be 'Anna'
echo $bella['Name']; // Should still be 'Bella'
echo $girl['Name']; // Should now be 'Bella' (in above example this will still be 'Anna')

Important notes:

• A workaround with a return value like $girl = &change(); is not a solution to my problem. It’s important that the global $girl is changed before the end of the change() function. (Reason being this is a problem inside a complex project with nested function calls all wanting to use the same global variables.)
• I am aware a workaround could be coded using the $GLOBALS array. However, I am specifically interested if this problem can be solved using the global keyword as seen in the example code. And if not, to know why this isn’t possible in PHP.
• Removing the &to make it $girl = $bella is also not a solution. The global $girl object needs to always be a reference to the original arrays defined at the start of the script. We cannot ever make copies / break references.

Question: Is this an impossibility in PHP when I use the global keyword? If so, can someone explain why? If not, can someone explain how to make this work?