Windows Central published a tip for the Surface Duo about how to enable app notification icons in Peek Mode.

Surface Duo tip: Enable app notification icons in Peek Mode

Make Peek Mode a little more useful with this handy tip. Out of box, the Peek Mode feature on Surface Duo doesn't seem to do all that much. It's designed to give you at-a-glance information about your phone just by opening the device a little bit, but by default it only shows you your date, time, and unlock status. However, Peek Mode can show you more than this, with the ability to enable app notification icons which show up below the date and time. This makes Peek Mode a little more useful, as it now shows you which apps you've missed notifications from. It still doesn't show the full notification like teased in this image from Microsoft, but it's a start.

Surface Duo tip: Enable app notification icons in Peek Mode