$cust_array = array(
    'tags' => $new_tag
);

$info = array('customer' => $cust_array );

$args = array(

    'headers' => array('Authorization' => 'Basic ' . base64_encode($credentials) ),
    'method' => 'PUT',
    'body' => json_encode( $info )

);

$response = wp_remote_get( '/admin/customers/#1234.json', $args );