Turns out that that was not the problem.

The attachment with the empty name is the original multipart/signed message attachment and normal.

The reason for this appears to be the "Content-ID", this is usually set for embedded attachments like images and not for attachments like PDF's.
This leads to the attachment being hidden, e.g. if you have embedded images you do not want them to show up in the list of attachments.

It is surprising though that Outlook itself is apparently intelligent enough to figure out when the attachment should be hidden and when not, but if we set the Content-ID in GpgOL it causes the file to be hidden, sometimes,..

After several experiments with attachment flags to get the same behavior outlook does for unsigned mails I could not find a way to set both the content-id and cause the attachment not to be hidden.

In the example I had the content-disposition was set to attachment and I think that Outlook also changes behavior based on that Header. So we now ignore Content-Id in case Content-Disposition: attachment is set.

This might break for some embedded images etc. But it's better to have broken display in some rare cases then hiding attachments altogether.

Curious as to whether there's been any update on this. GPG4Win is the only approved whole email + attachment encryption solution on this end, and we're having trouble with inline images showing up as attachments only in Outlook 2016 (using GPG4Win 4.0.2). Of course, as you said, at least the attachment isn't being lost; however it does make reading rich emails more difficult.