Is it possible to output the template name being used? Using a global variable or something similar? I am wanting to check which template is being used in a conditional.
I don't believe this is currently possible outside of the context of a Craft plugin. Inside of a plugin, you could probably do it through a Twig extension so that you have access to the template instance, where you could call $template->getTemplateName(), which is part of Twig's Twig_Template abstract class.