Client 192.168.1.1 has been rate-limited (current config allows up to 1000 queries in 60 seconds)

Below an nmtui example with 10.0.0.1 being my router and home.dehakkelaar.nl the domain configure in the Pi-hole DHCP service:

You can configure the default domain name displayed in the DHCP service settings.
Or "home.arpa", "internal" or "lan".

EDIT: I prefer home.arpa as its intended for this purpose and that name cant be stolen:

$ whois home.arpa.
[..]
contact:      technical
name:         Internet Assigned Numbers Authority (IANA)
[..]
remarks:      This domain is administered as part of the .ARPA zone
remarks:      management, described at https://iana.org/domains/arpa