How do you destroy a session in php?

the truth is once the user clicks the logout button the session will finish and he'll be rerouted towards the index.php here's my code

Customer.php

<?php 

session_start(); 
#include("Connection.php");
if (isset($_POST['submit'])) { 
$name = $_POST['customerName']; 
$_SESSION['user'] = $name; 
} 
if (isset($_SESSION['user'])) { echo "Hello {$_SESSION['user']}, welcome back"; }
else{echo "walang tao";}

$sql="INSERT INTO ORDERS(Name) VALUES('$name')";
mysql_query($sql);

session_destroy();
?>
<button><a href="Customer.php"></a></button>

which is in the index.php in which the user really wants to sign in again

<?PHP 
/* this must go before any html */ 
session_start(); 

if (isset($_SESSION['user'])) { 
header("location: Customer.php"); 
} 
?> 
     <div class="sign">
                    <h2>Welcome</h2>
                    <form action = "Customer.php" method = "POST">
                    Customer Name:<input type = "text" name="customerName">
                    <input type = "submit" name = "submit">
                    </form> 
session_start();
session_destroy();