Adding Fields to Registration

Hello I am trying to further extend the registration form. I have added both “first_name” and “last_name” as displayed by wordpress but for some reason it seems as though the update_user_meta is not saving whatsoever.

I have created the file wp-content/plugins/theme-my-login-custom.php
I have created wp-content/themes/child/register-form.php

This is the code I am using on the register page:

<div class="tml-user-first-last-name-wrap" style="margin-bottom: 25px;">
	        <span style="width:50%; padding-left: 25px; padding-right: 1px; float:left;"><input type="text" placeholder="First Name" name="first_name" id="first_name<?php $template->the_instance(); ?>" class="input" value="<?php $template->the_posted_value( 'first_name' ); ?>" size="20" />
	        <label for="first_name<?php $template->the_instance(); ?>"><?php _e( '', 'theme-my-login' ) ?></label>
	    </span>
	   	    <span style="width:50%; padding-left: 1px; padding-right: 25px; float:right;"><input type="text" placeholder="Last Name" name="last_name" id="last_name<?php $template->the_instance(); ?>" class="input" value="<?php $template->the_posted_value( 'last_name' ); ?>" size="20"  />
	   	    <label for="last_name<?php $template->the_instance(); ?>"><?php _e( '', 'theme-my-login' ) ?></label>
	   	</span>
	   	<br>
	   	</div>

This is the code I have in the custom file:

function tml_registration_errors( $errors ) {
	if ( empty( $_POST['first_name'] ) )
		$errors->add( 'empty_first_name', '<strong>ERROR</strong>: Please enter your first name.' );
	if ( empty( $_POST['last_name'] ) )
		$errors->add( 'empty_last_name', '<strong>ERROR</strong>: Please enter your last name.' );
	return $errors;
}
add_filter( 'registration_errors', 'tml_registration_errors' );

function tml_user_register( $user_id ) {
	if ( !empty( $_POST['first_name'] ) )
		update_user_meta( $user_id, 'first_name', $_POST['first_name'] );
	if ( !empty( $_POST['last_name'] ) )
		update_user_meta( $user_id, 'last_name', $_POST['last_name'] );
}
add_action( 'user_register', 'tml_user_register' );

Any ideas?

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