Menu block template doesn't provide the menu name at all

menu_name is available in menu templates, so you can easily add this by overriding menu.html.twig in your theme or via preprocessing.

The question is should core add this by default rather than relying on the user to add this themselves. This is a 9 year old task without much traction, so bumping it for visibility and to see if people have thoughts on if we should do this or not.

In the latest version of Drupal, the menu machine name is now included as a class for menus, providing a means to uniquely identify each menu.

@dawehner are you still seeing this issue?

Based on the last comments, I am closing this issue.