Hi,
When attempting to create an Azure DNS Public zone, customer may receive the error "The zone name {zone name} is not permitted. Please use a different zone name". Azure will perform a name validation for the Azure DNS Public zones against ICANN domains in Public Suffix list. In case the {zone name} value matches a Public Suffix without any additional label a Conflict error will be triggered.
For a complete list see https://publicsuffix.org/list/public_suffix_list.dat
In case you are the verified owner for such domain name and you are looking to move the whole hosting to Azure, you can contact Azure Support and they will proceed to create the zone from backend.
NOTE : "The zone {zone name} is not available." is a different error.
This error means that Azure DNS was unable to allocate name servers for this DNS zone. Try using a different zone name. Or, if you are the domain name owner you can contact Azure support to allocate name servers for you.