Not work Username UPDATE

<?php
session_start();
if(!isset($_SESSION['userid'])) {
    die('Bitte zuerst <a href="login.php">einloggen</a>');
}
$userid = $_SESSION['userid'];
if(isset($_GET['nameändern'])) {
$email = $_POST['email'];
$name = $_POST['name'];
$passwort = $_POST['passwort'];
$pdo = new PDO('mysql:host=localhost;dbname=', '', '');

$statement = $pdo->prepare("SELECT * FROM users WHERE email = :email");
$result = $statement->execute(array('email' => $email));
$user = $statement->fetch();
?>
    <html>
<head>
    <link href="/css/standart.css" rel="stylesheet">
  <title>Userbereich</title>
</head>
<body>

    <?php
    if ($user !== false && password_verify($passwort, $user['passwort'])) {
$statement = $pdo->prepare("UPDATE users SET 'name' = :name WHERE 'email' = :email");
$result = $statement->execute(array('name' => $name));
        $user = $statement->fetch();
}
else{
    die('Fehler');
    }
}
?>
 <html>
    <head>
    <link href="/css/standart.css" rel="stylesheet">
    <title>Userbereich</title>
     </head>
     <body>
     <nav>
<ul>
<li><a href="/">Home</a></li>
<li><a href="/login">Login</a>
<ul>
<li><a href="/login/login.php">Log In</a></li>
<li><a href="/login/registrieren.php">Registrieren</a></li>
<li><a href="/login/logout.php">Log Out</a></li>
</ul>
</li>
<li><a href="/login/geheim.php">aktuelle Seite</a></li>
<li><a href="/newsletter">Newsletter</a></li>
<li><a href="/fragen">Frage stellen</a></li>
<li><a href="/admin_area">Admin Area</a></li>
<li><a href="/userlist">Userlist</a></li>
<li><a href="/forum">Forum</a></li>
</ul>
</nav>
<br /><br /><br /><br /><br /><br />
     <h1> Hallo</h1>
     <h2>Username ändern:<br />
     <form action="?nameändern=1" method="post">
     E-Mail:<br />
     <input type="email" name="email" maxlength="40" size="40" /><br />
     Neuer Name:<br />
     <input type="text" name="name" maxlength="20" size="40" /><br />
     Passwort:<br />
     <input type="password" name="passwort" maxlength="250" size="40" /><br />
     Passwort erneut eingeben:<br />
     <input type="password" name="passwort2" maxlength="250" size="40" /><br />
     <input type="submit" name="ändern" value="ändern" />
     </form>
     </h2>
     </body>
</html>