Php Post name in Email Body - php

Question

Im new to php, i have a working contact form, but I would like to add the senders name into the body of the email I receive, this is what I have tried -
<?php
$to = "joedunlopburns#gmail.com";
$subject = "The Lantern Contact";
$name = $_REQUEST['name'];
$email = $_REQUEST['email'];
$message = "Message from $name\n$message";
$headers = "From: $email";
$sent = mail($to, $subject, $message, $headers) ;
?>
sorry if I'm being stupid!
Edit- Form added
<form id="contactform" method="POST" action="php/contact.php">
<input class="equal" type="text" name="name" autocomplete="on" placeholder="Name"><br/><br/>
<input class="equal" type="email" name="email" autocomplete="on" placeholder="Email Address"><br/><br/>
<input class="hide" type="email" name="fake">
<textarea class="equaltall" type="text" name="message" placeholder="Message"></textarea><br/><br/>
<input class="button" type="submit" value="Send">
</form>

Answer 1

It is better to use either $_POST and $_GET than $_REQUEST, and you are using $_POST for the body line, so I assume your data are sent using post.
When you receive any user input, you definitely have to test it. You can use filter_input to do that.
<?php
$to = 'me#gmail.com';
$subject = 'Contact';
$name = filter_input(INPUT_POST, 'name', FILTER_SANITIZE_STRING);
$email = filter_input(INPUT_POST, 'email', FILTER_SANITIZE_EMAIL);
$message = filter_input(INPUT_POST, 'message', FILTER_SANITIZE_STRING);
$body = $name; // why not use name in the following code?
$headers = "From: $email";
$sent = mail($to, $subject, $message, $body, $headers) ;
?>
I would also advise not to use the given email address as sender, because the message could then be considered as a spam, coming from a non related smtp server...