Just ran into this issue when I created a P2S VPN on my Azure Virtual Network – I downloaded the client and connected ok, but I realized I could only connect to my servers via IP, not by FQDN.
Checking my local IP settings, I realized that the DNS Server on my VPN connection was set to a public DNS server and not my Domain Controller / DNS server in Azure.
This wasn’t completely unexpected, because when I created the vnet I used Google DNS, and then I went back to the settings and changed it later once I had my DC set up.
It turns out that when you download the P2S VPN client from the Azure portal, it’s not really a client in the traditional sense (like the Cisco AnyConnect client) – it’s actually a number of config files that get installed to %appdata%\Microsoft\Network\Connections\Cm\connection-name\.
You can try editing the phonebook file as I’ve seen suggested around the web, but I don’t really like that solution – in order for this to work, you need to dial through the phonebook (pbk) file, and not just through the built in Windows VPN connection.
The answer, thankfully, is simple – just remove that VPN client and re-download the P2S VPN client from the Azure portal. Install it on your PC as before, and you’re good to go:
All better now!