U moet de variabele doorgeven in de verwijderlink. U moet <?php echo $contact['name']; ?>
naam waarde in verborgen veld of geef deze waarde door in URL
Vervangen
<td class="contact-delete">
<form action='delete.php' method="post">
<input type="hidden" name="name" value="">
<input type="submit" name="submit" value="Delete">
</form>
</td>
Met
<td class="contact-delete">
<form action='delete.php?name="<?php echo $contact['name']; ?>"' method="post">
<input type="hidden" name="name" value="<?php echo $contact['name']; ?>">
<input type="submit" name="submit" value="Delete">
</form>
</td>