- Rename the repository
- Create a new thing of the form you want
- Assuming they’re related, you can push to it
- If not, copy in the files and commit
If they aren’t technically related, but are practically, you can have some fun w/ git rebase or quilt to lift your commits from the one repo to the other.
Offhand, it sounds like you just want to rename the repo, create a new one, and commit the contents of the HEAD of the old repo into the new repo.
When you’re done, you can archive (or delete) the old repo.
The sequence of things isn’t particularly relevant here, you could start by creating a new repo, putting things the way you like it (and pushing!), and then do the renames last.