Can I have a custom URL for my Atlassian Cloud site?
JIRA, Confluence, and Bamboo Cloud will be offered on atlassian.net (so your service URL would be account.atlassian.net). The use of custom URLs is not supported at this time.
We do have a feature request, CLOUD-6999, for this in our public issue tracker with a more recent update comment from our Confluence product team - I invite you to vote and comment on this issue as well as watch the issue so that you are notified when it is updated. Atlassian uses jira.atlassian.com to help determine which features are popular or urgent enough to be added to our roadmap, so it's possible that we can address customer-requested functionality suggestions future releases.