PHP Form Not Showing Full Information on Submission - php

Question

I have a very simple form from a template with just three fields - Name - Email - Phone. When submitted the form works. BUT - if in the name field you have two words, e.g, John Smith - then it still submits but then everything after the first word gets truncated - so for the example, the mail received would show only "john" and not show "smith", neither will it show email or phone values. I have given my code samples below.. any help is highly appreciated.
PHP CODE BELOW
<?php
$to = 'x#gmail.com, y#gmail.com' ; // Put in your email address here
$subject = "Appointment Request"; // The default subject. Will appear by default in all messages. Change this if you want.
// User info (DO NOT EDIT!)
$name = stripslashes($_REQUEST['name']); // sender's name
$email = stripslashes($_REQUEST['email']); // sender's email
$phone = stripslashes($_REQUEST['phone']);
// The message you will receive in your mailbox
// Each parts are commented to help you understand what it does exaclty.
// YOU DON'T NEED TO EDIT IT BELOW BUT IF YOU DO, DO IT WITH CAUTION!
$msg = "Name: ".$name."\r\n"; // add sender's name to the message
$msg .= "E-mail: ".$email."\r\n"; // add sender's email to the message
$msg .= "Phone: ".$phone."\r\n"; // add sender's email to the message
$msg .= "Subject: ".$subject."\r\n\n"; // add subject to the message (optional! It will be displayed in the header anyway)
$msg .= "---Message--- \r\n";
$msg .= "\r\n\n";
$mail = #mail($to, $subject, $msg, "From:".$email); // This command sends the e-mail to the e-mail address contained in the $to variable
if($mail) {
echo 'Your message has been sent, we will be in touch shortly!'; //This is the message that will be shown when the message is successfully send
} else {
echo 'Message could not be sent!'; //This is the message that will be shown when an error occured: the message was not send
}
?>
HTML FORM CODE
<form role="form" onSubmit="return send_email();">
<div class="form-group">
<label for="exampleInputName">Name</label>
<input type="text" class="form-control" id="app_name" placeholder="Name" required>
</div>
<div class="form-group">
<label for="exampleInputEmail1">E-mail</label>
<input type="text" class="form-control" id="app_email" placeholder="E-mail" required>
</div>
<div class="form-group">
<label for="exampleInputPassword1">Phone</label>
<input type="text" class="form-control" id="app_phone" placeholder="Phone">
</div>
<button type="submit" class="btn btn-block btn-orange btn-Submit" onclick="ga('send', 'event', 'formsubmit', 'lp form', 'LP form');">Book my Free Consultation</button>
<small id="mail_msg"></small>
</form>
send_email() is actually in a JS file in a separate JS folder.. I have pasted the code below..
JS send_email
function send_email() {
var name=$("#app_name").val();
var email=$("#app_email").val();
var phone=$("#app_phone").val();
if(name=="")
{
$("#app_name").addClass("errors");
}
else
{
$("#app_name").removeClass("errors");
}
if(!validEmail(email))
{
$("#app_email").addClass("errors");
}
else
{
$("#app_email").removeClass("errors");
}
if(phone=="")
{
$("#app_phone").addClass("errors");
}
else
{
$("#app_phone").removeClass("errors");
}
if(name!="" && phone!="" && validEmail(email) )
{
$("#mail_msg").load("email.php?name="+name+"&email="+email+"&phone="+phone);
$("#app_name").val('');
$("#app_email").val('');
$("#app_phone").val('');
}
return false;
}
function validEmail(e) {
var filter = /^\s*[\w\-\+_]+(\.[\w\-\+_]+)*\#[\w\-\+_]+\.[\w\-\+_]+(\.[\w\-\+_]+)*\s*$/;
return String(e).search (filter) != -1;
}