If your server supports PHP, you could try this...
Make your page as you have, but change the action to this:
<FORM METHOD="POST" ACTION="send_mail.php">
Then create and upload this page, called send_mail.php:
$name = strip_tags($name);
$sendto = "you@youremail";
$subject = "Website contact form";
$message = "$name";
$from = "From: you@youremail";
mail($sendto, $subject, $message, $from);
$next_page = "index.html";
header("Location: $next_page");
That will send an email from your own email, to your own email with the $name variable, which was grabbed from your form. Then it will redirect back to your index page, or whatever you want.