This happened to me just now. What I did wrong was after updating the remote GitHub repository I did not create a new clone of it, rather continued to use the old one which still included the commits with old names. Once I have pushed from this old clone, the old commits were pushed and now there are duplicates.

If you have a backup of the repository before the rename, I think it is easier to get started again from the backup, just be careful not to repeat the same mistake - any repositories which are already cloned (by you or anyone else) need to deleted and cloned again after you manipulate their history.

I have also tried switching to the repository instead using TortoiseGit Switch/Checkout command (corresponds to git.exe checkout master -- command), and it seems to work as well, but you definitely need to make sure all cloned repositories are updated to match the remote version somehow, otherwise they will break it once you push from them.

As I was not careful enough to have a backup, this is what I have done to fix it: