$_SESSION["USER"] = $result["Gebruikersnaam"];

$test = $_SESSION['USER'];
$sql = "SELECT * FROM klant WHERE klant.Gebruikersnaam = $test";

<?php
if(isset($_SESSION['USER'])) {
    foreach ($db->query($sql) as $klant){ ?>
    <p><span class="glyphicon glyphicon-user"></span><?php echo $klant['Voorletters']. " " .$klant['Tussenvoegsel']. " " .$klant['Tussenvoegsel']; ?></p>
<?php
} } ?>