@ManuelDario, I’d suggest resubmitting the app for re-review after updating the tool annotations.
For openWorldHint: true, yes, use that when the tool connects to anything outside the local sandbox, like an external API, network resource, or third-party system.
For the developer name, you should be able to check it in the developer platform under Organization settings. Go to Verifications, then open the Verified dropdown to see the verified business name. That should be the name to enter exactly.
And agreed, having a checkbox to reuse the verified legal name would make this much simpler and less error-prone.
-Mark G.