You have conditional forwarding set up to have Pi-hole query the router at 10.0.1.1. If the router doesn't know the hostname or the PTR records then there's nothing that Pi-hole will be able to answer.
But 10.0.1.64 doesn't seem to be able to even access 10.0.1.1:
*** [ DIAGNOSING ]: Networking
[β] No IPv4 address(es) found on the eth0 interface.
[β] No IPv6 address(es) found on the eth0 interface.
[i] Default IPv4 gateway: 10.0.1.1
* Pinging 10.0.1.1...
[β] Gateway did not respond. (https://discourse.pi-hole.net/t/why-is-a-default-gateway-important-for-pi-hole/3546)
*** [ DIAGNOSING ]: Pi-hole log
-rw-r--r-- 1 pihole pihole 706733 Apr 8 17:48 /var/log/pihole.log
-----head of pihole.log------
Apr 8 16:31:58 dnsmasq[622]: started, version pi-hole-2.80 cachesize 10000
Apr 8 16:31:58 dnsmasq[622]: compile time options: IPv6 GNU-getopt no-DBus no-i18n no-IDN DHCP DHCPv6 no-Lua TFTP no-conntrack ipset auth DNSSEC loop-detect inotify dumpfile
Apr 8 16:31:58 dnsmasq[622]: using local addresses only for domain use-application-dns.net
Apr 8 16:31:58 dnsmasq[622]: using nameserver 10.0.1.1#53 for domain 1.0.10.in-addr.arpa
Apr 8 16:31:58 dnsmasq[622]: using nameserver 10.0.1.1#53 for domain home
Apr 8 16:31:58 dnsmasq[622]: using nameserver 1.0.0.1#53
Apr 8 16:31:58 dnsmasq[622]: using nameserver 1.1.1.1#53
Apr 8 16:31:59 dnsmasq[622]: read /etc/hosts - 7 addresses
Apr 8 16:31:59 dnsmasq[622]: read /etc/pihole/custom.list - 0 addresses
Apr 8 16:31:59 dnsmasq[622]: read /etc/pihole/local.list - 2 addresses
Apr 8 16:32:00 dnsmasq[622]: query[PTR] 1.0.0.1.in-addr.arpa from 127.0.0.1
Apr 8 16:32:00 dnsmasq[622]: config error is REFUSED
Apr 8 16:32:00 dnsmasq[622]: query[PTR] 1.0.0.1.in-addr.arpa from 127.0.0.1
Apr 8 16:32:00 dnsmasq[622]: config error is REFUSED
Apr 8 16:32:00 dnsmasq[622]: query[PTR] 1.1.1.1.in-addr.arpa from 127.0.0.1
Apr 8 16:32:00 dnsmasq[622]: config error is REFUSED
Apr 8 16:32:00 dnsmasq[622]: query[PTR] 1.1.1.1.in-addr.arpa from 127.0.0.1
Apr 8 16:32:00 dnsmasq[622]: config error is REFUSED
Apr 8 16:32:02 dnsmasq[622]: query[SOA] local from 127.0.0.1
Apr 8 16:32:02 dnsmasq[622]: forwarded local to 1.0.0.1
The Pi-hole DNS server itself seems to be functioning:
*** [ DIAGNOSING ]: Name resolution (IPv4) using a random blocked domain and a known ad-serving domain
[β] www.exelator.com is 0.0.0.0 via localhost (127.0.0.1)
[β] www.exelator.com is 0.0.0.0 via Pi-hole (10.0.1.64)
[β] doubleclick.com is 172.217.169.14 via a remote, public DNS server (8.8.8.8)
If the router does not respond with the host names to such requests, it is a bug of the router and Pi-hole can, unfortunately, not do anything about it.