Where is this information stored on a mac? I would like to edit these displayed texts without have to delete the folders and re-git the repository.
If you want to edit the git config, you can get it open from Sourcetree:
If the stuff you're looking to modify isn't in this file, you can also try the sourcetreeconfig file. That's located in <your_repo_'s_home_directory>/.git/sourcetreeconfig. .git is a hidden folder, so you'll need to use Terminal to get there or use Cmd+Shift+G in Finder to let you browse to that location.
Sorry that didn't seem to answer what you were trying to solve. You did ask "Where does SourceTree store repository configurations?" which is the answer originally provided.
As you found, what you really wanted to do (rename a repository locally) can be done simply by right-clicking or ctrl-clicking and selecting Rename. SourceTree saves the information about your repo browser (not the actual repo configs themselves) in ~/Library/Application Support/SourceTree/browser.plist.