In the latest update to BitNami Cloud Hosting, we added the ability to get a custom domain for your servers. During the process of creating a new server, you will now see a field where you can enter your own domain prefix. You will then be able to access your server at your_domain_prefix.bitnamiapp.
If you already have a BitNami Cloud Hosting account, you will see this new feature when you create a new server. If you do not yet have a BitNami Cloud Hosting account sign up for a free trial!