Based on my understanding of the scenario from your issue description.
The <app-name>.azurewebsites.net name is always assigned to your app as long as you don't delete it. The default certificate is provided and managed by Azure.
If you’re referring to other private certificate that you added (including App Service Certificate) for securing custom domain, if you have any bindings in App Service that use this certificate, they will become invalid. So, before removing the certificate, make sure that you have updated all the bindings.
Please check the doc for the FAQ and info about custom domain bindings:
How do I make sure that the app's IP address doesn't change when I make changes to the certificate binding?
Your inbound IP address can change when you delete a binding, even if that binding is IP SSL. This is especially important when you renew a certificate that's already in an IP SSL binding. To avoid a change in your app's IP address, follow these steps in order (refer the doc):
Just to highlight as a note - keep in mind that deleting an App Service certificate is an irreversible and final operation. So, make sure that you have a backup of the certificate before deleting it.
Kindly let us know how it goes with some more info about your exact requirement if the issue still persists.
Are you referring to this service/appp on Azure Marketplace or any other service?