Ok, your other thread says you've been reading documentation for Jira Server, which isn't much help for a Cloud system such as the one you are using.
You cannot change the base url yourself (there's an improvement logged for it).
For fully supported Cloud systems, support can change it, and you can raise a support request and they'll do it (but not frequently, so choose a good new site name for it, it won't change again for a long time unless you take the manual approach)
You've said you are on the Free version of Cloud, which is not supported for this, so you would have to do it the hard way:
in case you should not have resolved this issue meanwhile please let us know about details like Nic said.
In case you want to change your application or site name this article might be of help.
If this was not what you are looking for, please let us know,
it seems like I am trying to update the base url..
i followed the following:
I don't see any base url update options.
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