It is possible to change the small app icon on mobile courses from the default Rapid Intake icon to an image of your choice.  This is what the default icon looks like:

Here is where you go to change it:
After deploying the mobile course, open up the zipped file. Open the folder titled "resources" and double click on the folder titled "img." Look for the file called "icon.png." This is the file that is being used as the iphone app icon.

You will delete the default icon.png and replace it with a new file named icon.png. Make sure that the image you use has the same resolution and same format as the default icon.png (the default png image size is 72x72 pixels and 72 pixels/inch).

There are a few things that you need to consider:
If you try to deploy using the public link option or host the course on our server, the icon will get over-written every time unless you use the preview link.

Your best bet is to host the course on your own server so that the image file doesn't get over-written.