<?php
$arrays=array(array(
            "ID" => 250602,
            "NAME" => qwe
        ), array
        (
            "ID" => 250603,
            "NAME" => wer
        ), array
        (
            "ID" => 250629,
            "NAME" => sdf
        ), array
        (
            "ID" => 250629,
            "NAME" => xcv
        ),array(
            "ID" => 250629,
            "NAME" => fghfgh
        ),array
        (
            "ID" => 250601,
            "NAME" => pggd
        ), array
        (
            "ID" => 250601,
            "NAME" => dfgdfg
        ), array
        (
            "ID" => 250606,
            "NAME" => dfgdfg
        )
);

$final_array=array();
foreach($arrays as $sub_arr){ 
    $final_array[$sub_arr['ID']][]=$sub_arr['NAME'];       
}
print_r($final_array); 
?>

Array
(
    [250602] => Array
        (
            [0] => qwe
        )

    [250603] => Array
        (
            [0] => wer
        )

    [250629] => Array
        (
            [0] => sdf
            [1] => xcv
            [2] => fghfgh
        )

    [250601] => Array
        (
            [0] => pggd
            [1] => dfgdfg
        )

    [250606] => Array
        (
            [0] => dfgdfg
        )

)