Assuming that your variables are being passed correctly to this script, the 3rd line of your script should look like this:
$result = mysql_query("UPDATE Suppliers SET SuppName = '".$name."' WHERE SuppName = '".$pulldown."';") or die(mysql_error());
To set the column name that is to be update via a $_GET variable, your code could look like this:
$pulldown = CleanUserInput($_GET['q']);
$name = CleanUserInput($_POST['name']);
$column_name = CleanUserInput($_GET['column_name']);
$result = mysql_query("UPDATE Suppliers SET `".$column_name."` = '".$name."' WHERE `".$column_name."` = '".$pulldown."';") or die(mysql_error());
Of course this will the replace the value in the column for the variable $column_name
. Not sure if that is what you are trying to do.