The move to Resource Manager deployment in Azure is not so smooth.
This previously easy option is now very well hidden.
Forget everything Microsoft have poisoned your mind with for a second and remember how the internet actually works, they have finally followed reality.
The DNS names are now attached to the IP address, however, unlike all Microsoft products you do not set it under Properties, you set it under Configurations, confusingly there is also a Properties option.
TL:DR
1, Set a Public IP.
2, Select the IP Object.
3, Select Configuration.
4, Set the timeout and DNS name.
