Earlier quoted context omitted.
You can put your project in ~/work/my-go-project but then symlink it to ~/go/src/github.com/joshklien/my-go-project (assuming your $GOPATH is ~/go). But yes, with modules you don't need to do this anymore. go mod init github.com/joshklien/my-go-project
Where in your gopath are you supposed to put your source code if you never intend to upload it? All gopath tutorials I see say to put your github in the path like you did, and never say what to do if its not public.
If your project isn't intended to be uploaded (or is, but isn't intended to be consumed by other go projects as a go module), then you can make the project name whatever you want as far as I know.