You should look at the documentation. But If you dont find anything, you can add another catch :
<?php
try {
$stmt = $db->prepare("INSERT INTO tbl_user (id, name, password, question, answer) VALUES (NULL, :name, :password, :question, :answer)");
$stmt->bindValue(":name", $_POST['name']);
$stmt->bindValue(":password", $_POST['password']);
$stmt->bindValue(":question", $_POST['question']);
$stmt->bindValue(":answer", $_POST['answer']);
$stmt->execute();
echo "Successfully added the new user " . $_POST['name'];
} catch (PDOException $e) {
echo "DataBase Error: The user could not be added.<br>".$e->getMessage();
} catch (Exception $e) {
echo "General Error: The user could not be added.<br>".$e->getMessage();
}
?>
This must work because all exceptions of PHP plugins herits from the Exception native PHP class. (Since 5.0 if my memory is well).