Laravel Map key and values include duplicate records

Hi Mates, here is my input

$students = [
    [
	'id'	=> 1,
        'name' => 'John',
        'department' => 'Sales',
    ],
    [
	'id'	=> 2,
        'name' => 'Jane',
        'department' => 'Marketing',
    ],
    [
	'id'	=> 3,
        'name' => 'John',
        'department' => 'Sales'
    ],
];

so my desire output is

$studentLookup = [
    'Sales' => 'John',
    'Marketing' => 'Jane',
    'Sales' => 'Dave',
];

I tried this logic didn't work for me

$studentLookup = $students->reduce(function ($studentLookup, $student) {
    $studentLookup[$student['department']] = $student['name'];
    return $studentLookup;
}, []);

any help would be great. Thanks in advance.