I believe you will need either your own DNS or at least your own DNS proxy server.
This article provides a great break down of different Azure name resolution scenarios and the supported solution:
Name resolution for resources in Azure virtual networks
Specifically "Resolution of Azure hostnames from on-premises computers.", the stated approach is "...
Some VPS has the configuration of enable PPP service, so you can check it and enable the PPP item. The default settings may be disabled, this can cause error:
Couldn't open the /dev/ppp device: No such file or directory
vps config for ppp