The shortcode just displays a map, it doesn’t contain the POI info like address, icon, etc.
Normally, you can change the icon by just editing the map. Click on the POI, then click on the icon in the POI infowindow to change it.
There’s also an ‘automatic icon’ section in the MapPress settings screen, which can be used to default the icon based on tag/category, etc.
Please see the documentation for more details on both approaches above.