As far as I know it's not possible to set an alias/cname in the cloudapp.azure.com DNS zone.
But it's possible to use an alias/cname with a custom DNS domain:
https://learn.microsoft.com/en-us/azure/dns/tutorial-alias-pip
----------
(If the reply was helpful please don't forget to upvote and/or accept as answer, thank you)
Regards
Andreas Baumgarten