@Claudio Veneroni Azure DNS does not currently support purchasing of domain names. To purchase domains, you should use a third-party domain name registrar (Example- GoDaddy), who will typically charge a small annual fee. Once you buy the Domain, you can choose to use Azure DNS to host your DNS domain and manage your DNS records. More details here- https://learn.microsoft.com/en-us/azure/dns/dns-delegate-domain-azure-dns.
Once you buy a domain, you can then use this domain to point it to your VMs Public IP or DNS name. More details given here- https://learn.microsoft.com/en-us/azure/dns/dns-web-sites-custom-domain
Hope this helps. Please let us know if you have any further questions/concerns. Thank you!