Not yet. There's a request open to allow people to change their urls (and a wider one to allow people to use urls other than .atlassian.net), but at the moment, all you can do is buy a new Cloud system and move over to it.
I should have posted this link before - https://confluence.atlassian.com/cloudkb/changing-the-cloud-instance-url-address-or-migrating-to-a-new-cloud-instance-691011835.html
Nothing firm at all. I spoke to an Atlassian about it at Summit and the ability to change base-url by changing your Atlassian account settings is something they'd like to do (it won't go into the application), but her enthusiasm for loads of other changes being planned made me think it's a low priority. The wider "use non Atlassian urls" is a bigger piece and probably needs the change-url function working before they will do anything about it.
If you spend enough time as a Jira admin - whether you are managing a single, mid-sized instance, a large enterprise one or juggling multiple instances at once - you will eventually find yourself in ...
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