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.
So to summarise:
- git pull (locally cloned, to get latest changes)
- delete remote branch on BitBucket
- git fetch -p
- git branch -m <branch_name>
- git push -u <remote> <branch_name> (push to remote)
- create new branch from the branch in BitBucket
- delete the prev branch
Linux and Windows work differently with case sensitivity. While on linux you can have branch1 and Branch1, that will cause a conflict on windows. If you are a cross platform shop, you can configure bitbucket to ignore case on branch names.