In a File Manager, Open your Project root directory (where your .git folder is found).
Right click and go to:
TortoiseGit > Switch/Checkout
Ensure the Switch To Option to Branch. Then click the little button to the side of the drop down menu that is denoted by ...
A window will pop up showing the list of branches for you to choose.
Click on the one you want to rename.
Hit F2.
Rename your branch. Hit Enter. Click OK.
Now in the drop down menu, you’ll find that the branch-name has been updated.