Afaik you would have to register a domain, and point alias.example.com to alias.azure.com via a CNAME record.
But for ssl etc to work you would also have to get your vm setup so it "knows it's own (new) name" (alias.example.com).
[you could also use an A record with the ip, but I'm guessing guaranteeing sub-domain.azure.com points to the right ip is easier that updating the ip on updates etc to the vm]
But for ssl etc to work you would also have to get your vm setup so it "knows it's own (new) name" (alias.example.com).
[you could also use an A record with the ip, but I'm guessing guaranteeing sub-domain.azure.com points to the right ip is easier that updating the ip on updates etc to the vm]