I add a new project to github using egit by right clicking on the project and pushing it to the remote repository. This commits the project as below screenshot where the project name is committed at top level and bottom level. So blacked out section of attached image is same name.
When committing a new project do I just need to commit the files at level below the project name instead of committing the project name itself ?

The Egit tutorial mentions that you create a local repo first, then add as a remote your GitHub repo, and then push:
You should see your project files, and should never see or commit the
.gitcontent itself.