Best practice for renaming a GitHub App

We need to rename a GitHub app - both in the appstore and the marketplace.
What is best practice for doing so?
1: Just do it - what happens to existing installations?
2: Create new and delete old (after a long time)
3: Just rename the marketplace listing and live with the old name in the app store

The app inquestion is CodeImprover · GitHub Marketplace · GitHub

Regards Anders Product Manager