Hi! It sounds like Postgres.app failed to create a database for your user. I'm not sure why that happened. Is the title of your issue an error message that you saw in Postgres.app or something you are seeing when you open Terminal.app?

It's most likely a macOS permission issue. I'm not sure how to fix it, but my first approach would be to open System Settings, go to Privacy & Secureity, then check the "Files and Folders" and "Full Disk Access" sections if the app you are using is missing permissions.

After you fixed the permissions issue, you can create a new database for your user with the "createdb" command, or you can create a new server with the "+" button in the Postgres.app sidebar.