Running dig results in the following output (here I'm running dig on my PC):
> dig muellernet
; <<>> DiG 9.16.20 <<>> muellernet
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 50130
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;muellernet. IN A
;; Query time: 4 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: Sun Nov 07 07:22:27 CET 2021
;; MSG SIZE rcvd: 39
> dig muellernet.fritz.box
; <<>> DiG 9.16.20 <<>> muellernet.fritz.box
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 27290
;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;muellernet.fritz.box. IN A
;; ANSWER SECTION:
muellernet.fritz.box. 4 IN A 192.168.77.116
;; Query time: 4 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: Sun Nov 07 07:22:42 CET 2021
;; MSG SIZE rcvd: 65
> dig -x 192.168.77.1
; <<>> DiG 9.16.20 <<>> -x 192.168.77.1
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 4678
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;10.77.168.192.in-addr.arpa. IN PTR
;; Query time: 8 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: Sun Nov 07 07:23:20 CET 2021
;; MSG SIZE rcvd: 55
But running it on my Pi-hole Raspberry returns this:
> dig muellernet
; <<>> DiG 9.11.5-P4-5.1+deb10u6-Raspbian <<>> muellernet
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 21671
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 1, ADDITIONAL: 1
;; QUESTION SECTION:
;muellernet. IN A
;; ANSWER SECTION:
muellernet. 9 IN A 192.168.77.116
;; AUTHORITY SECTION:
muellernet. 9 IN NS fritz.box.
;; ADDITIONAL SECTION:
fritz.box. 9 IN A 192.168.77.2
;; Query time: 1 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: So Nov 07 07:26:59 CET 2021
;; MSG SIZE rcvd: 83
> dig muellernet.fritz.box
; <<>> DiG 9.11.5-P4-5.1+deb10u6-Raspbian <<>> muellernet.fritz.box
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 26264
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 1, ADDITIONAL: 1
;; QUESTION SECTION:
;muellernet.fritz.box. IN A
;; ANSWER SECTION:
muellernet.fritz.box. 9 IN A 192.168.77.116
;; AUTHORITY SECTION:
muellernet.fritz.box. 9 IN NS fritz.box.
;; ADDITIONAL SECTION:
fritz.box. 9 IN A 192.168.77.2
;; Query time: 1 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: So Nov 07 07:27:15 CET 2021
;; MSG SIZE rcvd: 84
> dig -x 192.168.77.116
; <<>> DiG 9.11.5-P4-5.1+deb10u6-Raspbian <<>> -x 192.168.77.116
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 44995
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 1, ADDITIONAL: 1
;; QUESTION SECTION:
;116.77.168.192.in-addr.arpa. IN PTR
;; ANSWER SECTION:
116.77.168.192.in-addr.arpa. 9 IN PTR MuellerNet.fritz.box.
116.77.168.192.in-addr.arpa. 9 IN PTR muellernet.fritz.box.
;; AUTHORITY SECTION:
116.77.168.192.in-addr.arpa. 9 IN NS fritz.box.
;; ADDITIONAL SECTION:
fritz.box. 9 IN A 192.168.77.2
;; Query time: 1 msec
;; SERVER: 192.168.77.2#53(192.168.77.2)
;; WHEN: So Nov 07 07:27:27 CET 2021
;; MSG SIZE rcvd: 143
You said:
Blockquote The reason for this may be that your Pi-hole host isn't able to request that from your FB's DHCP server, as that seems absent from your Pi-hole host machine's link
Were did get the out of the debug log? as you see running dig on the pi-hole machine returns proper results, because my fritz.box is configured as DNS host (i.e. in /etc/resolf.conf). So also running command host meullernet works fine on my pi-hole machine.