First and last name at registration page

I'd like to add first and last name to my registration form, since my payment gateway needs them to function as supposed.

I found registration.form.php and added two fields inside it like this:

<div class="alignleft">
			<label><?php _e('First Name','membership'); ?> <span>*</span></label>
			<input type="text" value="<?php echo esc_attr($_POST['first_name']); ?>" class="regtext" name="first_name">
		</div>

		<div class="alignleft">
			<label><?php _e('Last Name','membership'); ?> <span>*</span></label>
			<input type="text" value="<?php echo esc_attr($_POST['last_name']); ?>" class="regtext" name="last_name">
		</div>

But user First name and Last name are still empty?

Thank you