I successfully created the Azure Container App named my-app-name to host the Python Flask App.
The hostname for my app uses FQDN, so it looks like my-app-name.grayocean-1r2fd430h.centralus.azurecontainerapps.io.
I would like the hostname to be more user-friendly, for example my-app-name.azurecontainerapps.io (similar to the App Service, where it's named my-app-name.azurewebsites.net by default)
What should I do to make my custom hostname point to the Container App?
Unlike app service, in container apps there is a concept of an environment that groups all your apps that might need to communicate together whether it's for microservices or other designs you might have. the grayocean-1r2fd430h.centralus part is the unique part for your particular environment in this case.
However, From Container Apps you have 2 options here to give your app a custom domain:
1- You can use a different suffix for all the apps on your environment. i.e: replacing .grayocean-1r2fd430h.centralus.azurecontainerapps.io with some domain you might have, like .cornisto.io for example See https://learn.microsoft.com/en-us/azure/container-apps/environment-custom-dns-suffix for how to configure that.
2- You can assign custom domains per container app where each application can have its own set of custom domains that route to it. See this doc for how to set that up https://learn.microsoft.com/en-us/azure/container-apps/custom-domains-certificates
You could also use a service like Azure Front Door or API Management to proxy traffic to your application and the configuration of a custom domain would be on that end instead.