Question: `git mv` renames a file or directory in a repository. How do I rename the Git repository itself?

Answer: 
Rename `PRJ0.git` to `PROJ1.git`, then edit the URL variable located in the `.git/config` file of your project.
This is an extremely simple solution, though some may consider it "inelegant" or a "hack", and it belies my git inexpertise.

1. Verify that your local repo has everything committed and pushed (to remote origin).
2. Go to the website of the remote host (for example, <https://github.com/User/project-original-name>). Follow the host's instructions to rename the repo (will differ from host to host, but usually Settings is a good starting point). (For the purposes of this guide, suppose you renamed your repo to "project-new-name".)
3. Locally remove your whole repo (e.g., `rm -r project-original-name`).
4. Do a "fresh checkout": `git clone https://github.com/User/project-new-name`

NOTE: If another user of the repo doesn't follow these instructions, and just does a pull in the future, I have no idea what effect this will have.