Sending an email from PHP it shows headers: Mailed by: My.hostname.com

Question

Hello guys I am triying to send an email from PHP in HTML format, the email its sending correct but arrive with this headers: Email from PHP

If I send an email from Wordpress, the email shows good: Email from wordpress

What I need to do to send my email as wordpress do? Here my code:

<?php
$name    = $_POST["name"];
$email   = $_POST["email"];
$phone   = $_POST["phone"];
$product = $_POST["product_name"];
$country = $_POST["country"];




$template_File = "template.php";

$email_to = $email;
$subject ="asunto hoy";



$headers = "From: Roberto <fa.luis@outlook.com>\r\n";
$headers .= "MIME-Version: 1.0\r\n";
$headers .= "Content-Type: text/html; charset=UTF-8\r\n";



if(file_exists($template_File))

    $message = file_get_contents($template_File);
       else
die("unable to locate template file");


          $message = str_replace("#name#",   $name,    $message);
          $message = str_replace("#product#",$product, $message);
          $message = str_replace("#email#",  $email,   $message);
          $message = str_replace("#phone#",  $phone,   $message);

          if (mail($email_to, $subject, $message, $headers,))
            echo "listo";
            else
            echo "no listo";

echo $country;          
echo $message;
?>