Register icons to display on the Manage Plugins screen for plugins that aren't in the WordPress.org directory.

register-plugin-icons.php

<?php
/**
 * Register plugin icons.
 *
 * WordPress 4.9 introduced icons in the list table on the Manage Plugins
 * screen. The icons are pulled from the W.org update API. If an icon isn't
 * available, a generic plugin Dashicon is shown instead.
 *
 * @param  array $value Plugin update data.
 * @return array
 */
add_filter( 'site_transient_update_plugins', function( $value ) {
	$vendor_slug = 'example';                             // Unique vendor slug.
	$plugin_file = 'example/example.php';                 // Relative path to the main plugin file from the plugins directory.
	$plugin_icon = 'https://example.com/plugin-icon.png'; // URL to the plugin icon.
	
	$icons = array(
		'1x'      => '',
		'2x'      => '',
		'default' => $plugin_icon,
	);
	
	$plugin_slug = dirname( $plugin_file );

	if ( isset( $value->no_update[ $plugin_file ] ) ) {
		$value->no_update[ $plugin_file ]->icons = $icons;
	} elseif ( isset( $value->response[ $plugin_file ] ) ) {
		$value->response[ $plugin_file ]->icons = $icons;
	} else {
		$data = new stdClass;
		$data->id     = $vendor_slug . '/' . $plugin_slug;
		$data->slug   = $plugin_slug;
		$data->plugin = $plugin_file;
		$data->icons  = $icons;

		$value->no_update[ $plugin_file ] = $data;
	}

	return $value;
} );