Following the section Multiple Endpoints inManaging incoming traffic we can get endpoints of pattern:
<instance id>.app.pantaris.io
api-<instance id>.app.pantaris.io
As of today the instance id is a lengthy string, which works from the technical point of view, but is not really crisp and user friendly.
Are there plans to get “prettier” URLs, ideally supporting some extend of customization?
For example, an URL composed of segments derived from information such as<application>.<project>.<organization>.app.pantaris.io
The essence here is that the URL should be predictable by deriving it from other, human-understandable information.
No, there is nothing on plan to change this.
Changing one hash, to 3 UUIDs is not really prettier 
There is context information available in a different form. Find more information here.
Is there any way we can get some user friendly prttier url?
or to get a domain name and map it to the .app.pantaris.io url, like a kinda redirection ?
Technically spoken: You can use the external port feature and take care about authz & authn, domain, tls certs and setup a correct CNAME to our domain.
As there is one stack per project, you still would be required to use some kind of identifiers for the different instances.
So I do not recommend it, but you can go this way, but your are on yourself there.