You cannot rename a branch to Mercurial (or TortoiseHg, for that matter). Instead, you should start a new branch named production and place it in the current default branch.
You can do it in TortoiseHg 2.0, where you
- Click the line representing the working directory
- Press the go button
- Click to open a new branch
- Fill in the branch name and click OK
- Enter the commit message and click Commit.

This will create a new branch named production . The old default branch will remain, and you can add new functions there before combining them into production when they are stable.
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