So no, I can’t see a way to grab the name of your action. However, you can pass arguments to your callback:
$blog_id = get_current_blog_id();
$cron_name="import_blog_posts_in_network_daily_".$blog_id;
if ( !wp_next_scheduled( $cron_name) ) {
wp_schedule_event( time(), 'daily', $cron_name, array($blog_id) );
}
add_action( $cron_name, array($this, 'import_blog_posts_in_network') );
/*
public function import_blog_posts_in_network($blog_id) {
// do something for blog $blog_id
}
*/
Hope that helps!