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//Adding Registration fields to the form 

add_action( 'register_form', 'adding_custom_registration_fields' );
function adding_custom_registration_fields( ) {

	//lets make the field required so that i can show you how to validate it later;
	$firstname = empty( $_POST['firstname'] ) ? '' : $_POST['firstname'];
	$lastname  = empty( $_POST['lastname'] ) ? '' : $_POST['lastname'];
	?>
	<div class="form-row form-row-wide">
		<label for="reg_firstname"><?php _e( 'First Name', 'woocommerce' ) ?><span class="required">*</span></label>
		<input type="text" class="input-text" name="firstname" id="reg_firstname" size="30" value="<?php echo esc_attr( $firstname ) ?>" />
	</div>
	<div class="form-row form-row-wide">
		<label for="reg_lastname"><?php _e( 'Last Name', 'woocommerce' ) ?><span class="required">*</span></label>
		<input type="text" class="input-text" name="lastname" id="reg_lastname" size="30" value="<?php echo esc_attr( $lastname ) ?>" />
	</div><?php
}

//Validation registration form  after submission using the filter registration_errors
add_filter( 'woocommerce_registration_errors', 'registration_errors_validation' );

/**
 * @param WP_Error $reg_errors
 *
 * @return WP_Error
 */
function registration_errors_validation( $reg_errors ) {

	if ( empty( $_POST['firstname'] ) || empty( $_POST['lastname'] ) ) {
		$reg_errors->add( 'empty required fields', __( 'Please fill in the required fields.', 'woocommerce' ) );
	}

	return $reg_errors;
}

//Updating use meta after registration successful registration
add_action('woocommerce_created_customer','adding_extra_reg_fields');

function adding_extra_reg_fields($user_id) {
	extract($_POST);
	update_user_meta($user_id, 'first_name', $firstname);
	update_user_meta($user_id, 'last_name', $lastname);
	update_user_meta($user_id, 'billing_first_name', $firstname);
	update_user_meta($user_id, 'shipping_first_name', $firstname);
	update_user_meta($user_id, 'billing_last_name', $lastname);
	update_user_meta($user_id, 'shipping_last_name', $lastname);
}