I'm wondering if there is any way to know who has checked out my project hosted on GitHub? This would include people who have forked the project directly on GitHub, as well as people who may have cloned the repository using standard git clone
commands.
If by "checked out" you mean people who have cloned your project, then no it is not possible. You don't even need to be a GitHub user to clone a repository, so it would be infeasible to track this.