Hello @Julian Hüppauff - Sorry for the late reply. I'm not aware of any headers or any way for Functions to automatically know or maintain the origin hostname value given your scenario. I believe that Azure CDN has to send it explicitly, preferably via headers. With that said, I did come across the following blog post which seems to be achieving the same thing but leveraging DNS configurations to do so: PRESERVING ORIGINAL HOST WITH AZURE CDN AND APP SERVICES
I'll continue to dig in and update my answer with any new findings.