I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer. Accepted answers show up at the top, resulting in improved discoverability for others.
Issue: Is there a way to assign a DNS name in CSES like “CS Classic” allows you to do?
Solution: Customer shared - I have found the answer by clicking on the IP address then configuration and then - Enter the DNS name label
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