Do not check for plugin or theme update. Include in core functionality plugin.

don't-update-plugin.php

/**
 * Don't Update Plugin
 *
 * @since 1.0.0
 *
 * This prevents you being prompted to update if there's a public plugin
 * with the same name.
 *
 * @author Mark Jaquith
 * @link http://markjaquith.wordpress.com/2009/12/14/excluding-your-plugin-or-theme-from-update-checks/
 *
 * @param array  $r, request arguments
 * @param string $url, request url
 * @return array request arguments
 */
function cws_hidden_plugin( $r, $url ) {
	if ( 0 !== strpos( $url, 'http://api.wordpress.org/plugins/update-check' ) ) {
		return $r; // Not a plugin update request. Bail immediately.
	}
	$plugins = unserialize( $r['body']['plugins'] );
	unset( $plugins->plugins[ plugin_basename( __FILE__ ) ] );
	unset( $plugins->active[ array_search( plugin_basename( __FILE__ ), $plugins->active ) ] );
	$r['body']['plugins'] = serialize( $plugins );
	return $r;
}
add_filter( 'http_request_args', 'cws_hidden_plugin', 5, 2 );