You would need to do the renaming locally in your repository. But before you do that, delete the branch in Bitbucket, do a fetch in your local clone to update it (if doing it from Sourcetree, make sure you check prune tracking branches, from cmd use git fetch -p). Then you can rename the branch and push it back to Bitbucket.
Officially I don't see a way to rename them, but we have had to do that in some cases. What we do is basically the following
We have branch bugfix/JIRA-1 and want to rename it to bugfix/JIRA-100
All I usually do is take bugfix/JIRA-1 and create a branch off of that called bugfix/JIRA-100
At that point 1 and 100 should be identical.
I can then delete bugfix/JIRA-1.
You could do this via the bitbucket UI or command line as GErhard_Pretorius linked above. I personally like the UI in this case as it saves me the step of having to push to origin.
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