Hi @Max ,
When you mean setting up your own DNS Server are you referring to delegation of your child domain to the parent domain wherein it has its own Name Servers? If yes then the following document has the steps mentioned: https://github.com/Huachao/azure-content/blob/master/articles/dns/dns-domain-delegation.md#delegating-sub-domains-in-azure-dns.
Hope this helps. Do let me know in case of any additional questions or concerns that i can assist you with.
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.