In the first comment of bug 1577316, you can see how a desktop notification from an extension looks like (via the Notification API). There are two features of interest:

• a cog from where the notification can be disabled and/or configured.
• the GUID that identifies the extension

Due to an implementation detail, notifications from the browser.notifications API look different: neither of these two features are shown (actually, it briefly was, but the change was reverted in bug 1577316 because the cog was non-functional).

Thanks to the work in bug 1589693, it becomes viable again to show the cog on notifications from the browser.notifications API.

I think that ideally, the GUID should either be replaced with the extension name, because the GUID is meaningless for almost every user. This suggestion is consistent with how we render the chip in the location bar for moz-extension:-URLs and the window bar of extension popup windows.

If we make this change, then the UI from the Notification and browser.notifications APIs are consistent, and always include controls to toggle the visibility of notifications. This is probably good for users.
On the other hand, I can imagine that extension authors may prefer a minimalistic notification (without cog or extension name). I think that the benefits outweigh this latter concern, and I'll leave this bug open initially to solicit feedback.