Yes. The icon and a name are yours by default, but you also can fully brand the app so that links lead to you own domain, not Mobsted domain.
This is done through using proxy. This feature is build in our platform for all plans. You will need to make additional actions on your side, though. You have 2 choices - create a subdomain for your domain, i.e. "NNN.yourdomain.com" or create a folder like "yourdomain.com/NNN".
For more info read an article - Branding apps to your domain