Router not resolving pi-hole hostname

Can you post results for below two on the Macbook:

nslookup debianserver 192.168.1.100

nslookup debianserver

And on Pihole:

hostname -f

cat /etc/hosts

cat /etc/pihole/local.list

If you have dhcpcd5 installed that comes with Pi-hole:

pi@noads:~ $ apt policy dhcpcd5
dhcpcd5:
  Installed: 1:6.11.5-1+rpt7
  Candidate: 1:6.11.5-1+rpt7

And active:

pi@noads:~ $ sudo service dhcpcd5 status
[..]
   Active: active (running) since Sun 2019-09-08 22:28:43 CEST; 1 weeks 0 days ago
[..]

IP settings belong in /etc/dhcpcd.conf:

pi@noads:~ $ tail /etc/dhcpcd.conf
[..]
interface eth0
  static ip_address=10.0.0.2/24
  static routers=10.0.0.1
  static domain_name_servers=127.0.0.1

And /etc/network/interfaces should resemble below:

pi@noads:~ $ cat /etc/network/interfaces
# interfaces(5) file used by ifup(8) and ifdown(8)

# Please note that this file is written to be used with dhcpcd
# For static IP, consult /etc/dhcpcd.conf and 'man dhcpcd.conf'

# Include files from /etc/network/interfaces.d:
source-directory /etc/network/interfaces.d

auto lo
iface lo inet loopback

iface eth0 inet manual