Hi,
To find the template name of any report, what you have to do is that, activate the developer mode and navigate to settings -> technical -> reporting -> reports, search for the report that you need, in this case search invoice, then click and open the report.

Once it is opened, in the top right, you can see a smart button named Qweb Views, click on it, you will all the templates(main and inherited)

Also there is a field named Template name, you can get the value from there also.

Thanks