WordPress – WooCommerce custom payment gateway is not showing in checkout

There are some mistakes and missing things in your code. Try the following revised code:

<?php
/**
 * Plugin Name: Noob Payment for Woocommerce
 * Plugin URI: https://omukiguy.com
 * Author Name: Laurence Bahiirwa
 * Author URI: https://omukiguy.com
 * Description: This plugin allows for local content payment systems.
 * Version: 0.1.0
 * License: 0.1.0
 * License URL: http://www.gnu.org/licenses/gpl-2.0.txt
 * text-domain: noob-pay-woo
*/ 

defined( 'ABSPATH' ) or exit;

if ( ! in_array( 'woocommerce/woocommerce.php', apply_filters( 'active_plugins', get_option( 'active_plugins' ) ) ) ) {
    return;
}

add_action( 'plugins_loaded', 'noob_payment_init', 11 );
function noob_payment_init() {
    if( class_exists( 'WC_Payment_Gateway' ) ) {
        class WC_Noob_pay_Gateway extends WC_Payment_Gateway {
            public $instructions;

            public function __construct() {
                $this->id   = 'noob_payment';
                $this->icon = apply_filters( 'woocommerce_noob_icon', plugins_url('/assets/icon.png', __FILE__ ) );
                $this->has_fields = false;
                $this->method_title = __( 'Noob Payment', 'noob-pay-woo');
                $this->method_description = __( 'Noob local content payment systems.', 'noob-pay-woo');

                $this->title = $this->get_option( 'title' );
                $this->description = $this->get_option( 'description' );
                $this->instructions = $this->get_option( 'instructions' );

                $this->init_form_fields();
                $this->init_settings();

                add_action( 'woocommerce_update_options_payment_gateways_' . $this->id, array( $this, 'process_admin_options' ) );
            }

            public function init_form_fields() {
                $this->form_fields = apply_filters( 'woo_noob_pay_fields', array(
                    'enabled' => array(
                        'title' => __( 'Enable/Disable', 'noob-pay-woo'),
                        'type' => 'checkbox',
                        'label' => __( 'Enable or Disable Noob Payments', 'noob-pay-woo'),
                        'default' => 'no'
                    ),
                    'title' => array(
                        'title' => __( 'Noob Payments Gateway', 'noob-pay-woo'),
                        'type' => 'text',
                        'default' => __( 'Noob Payments Gateway', 'noob-pay-woo'),
                        'desc_tip' => true,
                        'description' => __( 'Add a new title for the Noob Payments Gateway that customers will see when they are in the checkout page.', 'noob-pay-woo')
                    ),
                    'description' => array(
                        'title' => __( 'Noob Payments Gateway Description', 'noob-pay-woo'),
                        'type' => 'textarea',
                        'default' => __( 'Please remit your payment to the shop to allow for the delivery to be made', 'noob-pay-woo'),
                        'desc_tip' => true,
                        'description' => __( 'Add a new title for the Noob Payments Gateway that customers will see when they are in the checkout page.', 'noob-pay-woo')
                    ),
                    'instructions' => array(
                        'title' => __( 'Instructions', 'noob-pay-woo'),
                        'type' => 'textarea',
                        'default' => __( 'Default instructions', 'noob-pay-woo'),
                        'desc_tip' => true,
                        'description' => __( 'Instructions that will be added to the thank you page and odrer email', 'noob-pay-woo')
                    ),
                ) );
            }

            public function process_payments( $order_id ) {
                $order = wc_get_order( $order_id );

                // Some other code
            }
        }
    }
}

add_filter( 'woocommerce_payment_gateways', 'add_to_woo_noob_payment_gateway');
function add_to_woo_noob_payment_gateway( $gateways ) {
    $gateways[] = 'WC_Noob_pay_Gateway';
    return $gateways;
}

add_filter( 'plugin_action_links_' . plugin_basename( __FILE__ ), 'woo_noob_payment_gateway_plugin_links' );
function woo_noob_payment_gateway_plugin_links( $links ) {
    $plugin_links = array(
        '<a href="' . admin_url( 'admin.php?page=wc-settings&tab=checkout&section=noob_payment' ) . '">' . __( 'Configure', 'noob-pay-woo' ) . '</a>'
    );
    return array_merge( $plugin_links, $links );
}

Now it should be displayed in checkout, when enabled…