I kind of remember that the windows version saved files as "[Artist] - [Album title].jpg" when using "Save to file..." from the albumart context menu. The macOS version currently always defaults to "folder.jpg".
Would be awesome if users could even choose the automatic naming scheme themselves (similar to the audio file naming patterns).
In the WIndows version you can set the format string for the exported image in File>Options>Tag-Sources.
See if there is a similar option in the Mac version.
It's not. And to be honest, that is IMHO the absolutely wrong place to put it from a UX perspective. Under "Tag sources" I'm expecting all the data sources where I can get tag data from, not a setting how I use this data to process a file. But maybe that's only me... 
Yes, users always need some time to learn that this setting also is relevant for the cover-naming from the context-menue.
But:
It is relevant in tag-sources (Utils-button) if you enable that the cover shall be saved as a file.
Ah, I get it. Tricky UI dilemna incoming: Do I introduce two different settings for basically the same thing and also have to find a proper location in the app for both of them - or do I only provide a single setting and have to live with the fact that a part of the users won't find it there according to their mental model? Difficult.
Nevertheless, it's currently not yet possible in the macOS version, regardless of the location question. 
@Florian Isn't this feature now implemented as part of the Export Cover action? If so, might be worth noting it here and closing the thread. THANK YOU for implementing that action. Made me a happy camper. 
I didn't even notice that this action was available now (that will teach me to skim release notes 
). I was searching the forums and this was the only post I found for the Mac version.
It's something different — Mp3tag for Mac v1.10 adds support for user-defined cover filename presets for saving artwork from the Tag Panel (available from Settings → Export → Cover Filename).
Previously, saving an album cover from the Tag Panel (via the context menu or drag and drop) used folder as the default filename. Settings → Export now allows you to configure the default name, including support for placeholders.