In GitHub Desktop, there isn’t really a home page to go back to.
While you’re in a repository its name will be in the top left corner of Desktop, in the section called “Current Repository”.
If you click the arrow in that section it will show you a list of the repositories that you have in GitHub Desktop. This is perhaps where you are getting confused, as you might expect it to show you all of your repos from GitHub? Actually, it’s only showing you the ones you have locally.
If you click the “Add” button that is next to the filter box, and then “Clone Repository”, that will show you a list of all the repositories you have access to on GitHub - not just your own, but also repos you are a collaborator on, or have access to via an organization!
You can filter the list to quickly find the specific repo you want, and then clone it down to GitHub Desktop, and then it will be visible in the list you are used to looking at.
I hope that clarifies things!