The company I work for has been acquired, and we need to change the sub-domain to match the new company's name.
Most references I found are very old and say it's not possible in the onDemand/Cloud version; or say to contact support, which only seems possible by asking a question on this public forum.
Edited in response to a proposed answer:
On the system setting page, I checked both the General Settings and Advanced settings. Base Url was not an editable field on either. My understanding is that if you install JIRA on your own servers, Base Url can be edited under System Settings, but not on the onDemand / Cloud version.