Ah, the title of the module. to me "module name" meant "jrAudio" "jrVideo", I thought you wanted that.
In the {debug} output there is probably a {$_mods} section with all of the active modules and their data. You can target the 'module_name' from that section by giving it the module name you're getting, eg:
{$_mods.jrAction.module_name}
will output "Timeline" or
{$_mods.jrAudio.module_name}
will output "Uploaded Audio" if thats what its set to in the ACP.
So using this structure, you can pass in the variable that contains your 'jrAudio' and get back the display name for the module.
Try:
{$_mods[$item.action_data.comment_module].module_name}
Related docs:
Docs: "{debug}"
https://www.jamroom.net/the-jamroom-network/documentation/development/1477/debug
Docs: Smarty Docs
http://www.smarty.net/docs/en/index.tpl