Drupal - What is the procedure for deleting a project in drupal.org?

If your project contains code usually it is not deleted. In that case, you can select as Project classification Unsupported and as a Development status Obsolete.

You can always create a post in the Drupal.org webmasters issue queue explaining your situation and requesting the project deletion.

But I can tell you that if you have people using your module, they will not delete the project.

The official procedure is asking for the project to be deleted in the Drupal.org webmasters issue queue by creating a new issue. The project is not deleted if there is committed code, or there are issues for that project.

If the project has committed code, and you just wanted to change short name to the project, since project short names cannot be changed once the project is created, just mark the project as unsupported, after you created the new project, and committed code.

Possibly, you should also create a stable release for the new project, so the maintainers of those sites using the old project who receive a warning about the project not being anymore supported would find a production release to use.
Together this, you should also add a link to the new project in the old project page.

Disclaimer

I am a Drupal.org webmaster, and what I described is the procedure we follow when handling requests for deleting projects, and what the Drupal.org Infrastructure Team suggests to the webmasters who handle those requests.