trouble with php server adding variable to my contact forms

Question

Hi I have added some input variables in my contact form and I can't find how to add them to my server.php I attempted multiple things such as adding $phone and other variables I just don't know where to import them from the answer might be closer than I expected.

here my original contact form

<div class="form-group">
   <div class="input-group">
      <label for="name" class="input-group-addon">
      <span class="glyphicon glyphicon-user"></span>
      </label>
      <input type="text" placeholder="Nom" class="form-control col-xs-12" id="name" name="name" data-error="Valid Name" required>
   </div>
   <span class="help-block with-errors"></span></div><!-- phone--><div class="form-group">
   <div class="input-group">
      <label for="phone" class="input-group-addon">
      <span class="glyphicon glyphicon-earphone"></span>
      </label>
      <input type="tel" placeholder="Telephone or email" class="form-control col-xs-12" data-error="Valid phone" id="phone" name="phone" pattern="[0-9]{3}-[0-9]{3}-[0-9]{4}">
   </div>
   <span class="help-block with-errors"></span></div><!-- Who to contact --><div class="form-group">
   <div class="input-group">
      <label for="person" class="input-group-addon">
      <span class="glyphicon glyphicon-user"></span>
      communiqué avec: <b>(optionnel)</b>
      </label>
      <input list="persons" name="person" id="person">
      <datalist id="personnes">
         <option value="person1">
         <option value="person2">
         <option value="person3">
         <option value="person4">
      </datalist>
   </div>
   <span class="help-block with-errors"></span>
   </div>
   <!-- Custom time --><div class="form-group"><div class="input-group"><label for="appt" class="input-group-addon"><span class="glyphicon glyphicon-time"></span>
Calling time:<b>(optional)</b></label><input type="time" placeholder="E-mail or phone" id="appt" name="appt"></div>                                                      
<span class="help-block with-errors"></span></div>
<!-- Message --><div class="form-group">                                   
<div class="input-group"><label for="message" class="input-group-addon"><span class="glyphicon glyphicon-comment"></span></label><textarea class="form-control" rows="4" id="message" name="message incorrect" placeholder="Message" data-error="Message" required></textarea></div>                            
<span class="help-block with-errors"></span></div>
<div><button type="submit" id="submit" data-error="enter message" class="btn btn-custom btn-block">Send</button></div>

Here my original server .php

<?php

$errorMsg = "test";

// NAME
if (empty($_POST["name"])) {
    $errorMSG = "Name is required! ";
} else {
    $name = $_POST["name"];
}

// EMAIL
if (empty($_POST["mail"])) {
    $errorMSG .= "Email is required ";
} else {
    $mail = $_POST["mail"];
}

// MESSAGE
if (empty($_POST["message"])) {
    $errorMSG .= "Message is required ";
} else {
    $message = nl2br($_POST['message']);
}

// Phone
if (empty($_POST["phone"])) {
    $errorMSG .= "phone is required ";
} else {
    $phone = $_POST["phone"];
}

// Change to your E-mail && Subject
$EmailTo = "[email protected]"; // change to your E-mail here
$Subject = "contact form";     // change to the subject you want

// prepare email body text
$Body = '<b>Name:</b> '.$name.' <br><b>E-mail</b> '.$mail.' <p>' .$message.'' .$phone.'</p>';
$headers  = 'MIME-Version: 1.0' . "\r\n";
$headers .= 'Content-type: text/html; charset=utf-8' . "\r\n";
$headers .= 'From: ' . $mail . "\r\n";

// send email
$success = mail($EmailTo, $Subject, $Body, $headers);

// redirect to success page
if ($success && $errorMSG == ""){
   echo "success";
}else{
    if($errorMSG == ""){
        echo "Something went wrong :(";
    } else {
        echo $errorMSG;
    }
}

Thanks!