Thank you for reaching out.
I understand you wish to assign a DNS name to your VM's private IP as you do not have Public IP assigned to your VM.
The way to do this using Azure Private DNS
Azure Private DNS provides the following capabilities:
- Automatic registration of virtual machines from a virtual network that's linked to a private zone with autoregistration enabled. Virtual machines get registered to the private zone as A records pointing to their private IP addresses.
You can go through this documentation to understand how the DNS name resolution is scoped.
You can go through this tutorial to create private DNS zones.
Hope this helps! Please let me know if you have any additional questions here. Thank you!
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.