Setting up a custom domain with an Azure Function app
Copying from my answer on MSDN forum:
Indeed, custom domains are not yet supported for Dynamic Function plans. This support will come a bit later (no clear ETA to share at this point).
Thanks to @David Ebbo I figured out how to do this for a Function App running in a consumption plan (e.g. Y1). Here is the MSFT docs article:
https://docs.microsoft.com/en-us/azure/app-service/scripts/cli-configure-custom-domain
It seems that it cannot currently be done via the Azure Portal GUI and instead you must use Azure CLI to run the commands. It's easy to do directly from that article page using the "Try It" link to the embedded azCLI.