Ok, you seem to mix serveral aspects. Let me try to explain.
Commit meta data
Git requires a name and an email address for commit meta data. The settings page in the question shows exactly that. Here you can set up the name and email address which is used as the author and committer name of commits (this also might be needed for merges). These two settings are not used for authentication, they are just meta data for commits.
The global Settings dialog
The TortoiseGit settings dialog provides different configuration options depending on from where it is invoked. In your case it is invoked "globally" and is not associated to a specific repository. - You can see that there is no path shown in the title bar.
The working tree specific settings dialog
When the settings dialog is openend from a working tree, you see the path in the title bar and also some more options:
For example you can see the new point "Remotes", there you can configure the remote repositories from which you can easily pull and fetch as well as push to. The "origin" remote repository is likely to be already filled in when you cloned a repository.
Normally, no credentials are stored here -- just the URL to the remote repository and maybe an SSH key. In order to store HTTPs credentials see TortoiseGit save user authentication / credentials, in order to clean up stored credentials see Remove saved credentials from TortoiseGit.
Besides that, on the "Git" page, there now is also the "Local" radio button enabled. This can be used when you want to use different user name and email address meta data for different working trees (the values set under Local will override the ones specified under Global). You can always click oin the "Effective" radio button to see the effective values for a specific working tree.
