I don't know how to do it in mysql but you could always use an associative array and do this in your code
$arrMonth = array(
"JANUARY" => "<january in dutch>,
"FEBRUARY" => "...
then in your query
$strQuery = "
SELECT UCASE(DATE_FORMAT(datumtoeg, '%M')) as month_name
FROM organisatie
WHERE orgcode = '$organisatie'";
then when you do your echo
echo $arrMonth[$row["month_name"]];
so if $row["month_name"] == "JANUARY", you will get back whatever is in that associative array value as the translation.. sorry i don't know any dutch..
p.