PHP Form issues with action and echoing result - php

Question

I am trying to get a simple two-field form to submit to an email address and then echo a "thanks for registering your interest" below the form (or instead of the form).
FYI, this is on a WordPress template file.
Here is the code, including the form:
<form action="<?php echo htmlspecialchars($_SERVER["PHP_SELF"]);?>"
method="POST" autocomplete="on" id="register-form">
<input type="text" name="name" placeholder="Name"/>
<input type="email" name="email" placeholder="Email address"/>
<button type="submit" name="submit" class="button">Send
<img src="<?= get_image('icon-arrow-right-tiny.svg'); ?>"/></button>
</form>
<?php
if (isset($_POST['submit'])) {
// validate the email address first
$email = filter_input(INPUT_POST, 'email', FILTER_VALIDATE_EMAIL);
// process the form only if the email is valid
if ($email) {
$to = 'info#example.com'; // where you want to send the mail
$from = 'info#mydomain.com';
$subject = 'Website Submission';
$message = 'Name: ' . $_POST['name'] . "\r\n\r\n";
$message .= 'Email Address: ' . $_POST['email'] . "\r\n\r\n";
$headers = "From: $from\r\nReply-to: $email";
$sent = mail($to, $subject, $message, $headers);
} ?>
<p style='color: #fff; font-size: 14px;'>Thank you for registering your interest.</p>
<?php
}
?>
At the present time, the form does get sent, and the page does echo "Thank you for registering your interest" underneath the form, however it does not seem to be returning us to the correct page when you click the submit button.
Any ideas?

Answer 1

Thank you for all of your contributions. I have worked out the problem, and will share here for anybody else who comes here to find the answer.
WordPress has something important reserved for the "name" parameter, and thus you can't use it in PHP-based forms. Changing the parameter name from "name" to something else resolved the issue.
Additionally, WordPress also has the following names reserved and you cannot use them in forms - "day" "month" and "year".

Answer 2

I have check your code i think you have use color code #fff i.e. for the message.
Please try to make black or any other color rest of code are working.
:)
Thank you for registering your interest.

Answer 3

You have to put a php code below your Thank you message.
header("location:$_SERVER["PHP_SELF"]);exit;