When i perform a nslookup, i get an answer like 127.0.1.1 (taken from the /etc/hosts of the Pi-hole following the usual "hosts,bind order"); so i can't reach the WebUI using the Hostname.
I have now created a "Local DNS Record" which points to the right IP-Adress.
I know that's a little bit weird to administrate a DNS Server using it's own Services. But Adminal Ackbar also think "It's a trap"...?!?
Thanks for the screenshot.
Now, that reveals that you are using pihole as a name. pihole is not a name that Pi-hole creates - it's entirely up to you to correctly set up resolution for that name.
A default Pi-hole installation will create the appropriate definitions to make its web UI available at http://pi.hole/admin:
When it comes to DNS resolution of the machine that hosts your Pi-hole, you have a choice of making use of Pi-hole or some public DNS, see Correct Resolv.conf entry in pihole 5.11.