I have checked with Fairphone support, and they confirm the following:
[…] Our technical team confirmed this is a known behavior when VoLTE or Wi-Fi Calling is enabled on a network that is not yet officially supported. Even though your device supports these features and IMS shows as “Registered,” the absence of an official configuration profile for the carrier can cause these caller ID problems.
In essence, the providers are not yet supported, and are missing IMS profiles. I created a ticket here on /e/os GitLab, but not sure who’s handling modem configurations in terms of software.
Also, I have since changed my network provider which resolved the issue. It works for Ice AS (which partly uses its own network combined with Telias network). The issue seems to be with Telenor network in Norway.