I'm an app developer with a demo store and have the same problem right now... I've not found a way to do this and I don't believe it is possible. Hopefully someone will let us know otherwise. If you are paid then you can add your own domain but the myshopify.com will probably stay the same.
Hope I'm wrong!
GMKnight, what I need is exactly that you said: change a shopify domain for another shopify domain. Ex.: 123.myshopify.com to 456.myshopify.com. When my store starts selling I'll probably buy a .com domain and integrate to shopify but I want to ensure that the domain I want will not be registered.
If there's no way to do that I will have to create a new account with a new myshopify domain, but I dont know if I can save my actual page (still developing) and load on the new domain.
Personally I'd recommend upgrading and setting up your domain as one of the first things to do.
At the end of the day it doesn't matter what the myshopify.com domain is if you buy your own and use that (trust me, I have two stores with the wrong domains - but all the customers see the domains I purchased).