Rename the keys of children in a 2-dimensional array

Starting with this array

$start_array = [
    ["date" => "2012-05-01", "revenue" => 100],
    ["date" => "2012-05-02", "revenue" => 200],
];

How can I rename the keys date and revenue in the child arrays so I get this:

$final_array = [
    ["x" => "2012-05-01", "y" => 100],
    ["x" => "2012-05-02", "y" => 200],
];

Here is my attempt which works, but is messy:

$final_array = array();
$max = count($start_array);
for ($j = 0; $j < $max; $j++) {
    $final_array[] = [
        'x' => $start_array[$j]['dateid'],
        'y' => $start_array[$j]['ctrl_version_revenue'],
    ];
}