Configuring custom DNS in Azure Functions:
- Create a Function App
- Create a function with HTTP Trigger (Make sure to select the appropriate Authorization Level) -- Use code or portal of your choice of IDE
- Deploy your code to the functions app
- Goto FunctionApp -->TLS Settings-->Upload your Domain certificate
- Go to FunctionApp-->Custom DNS-->Add the mapping (You must complete recordset into your DNS pointing to the function as CNAME)
- Complete secure binding
You can now browse to your <DNS>/api/<YOUR HTTP FUNCTION>
P.S: If you run your function in multiple regions then create a TXT record and then use a Global Load balancer such as Traffic Manager or Front Door name to map to CNAME