Four solutions depending on your version and choices
Control Center -> Network --> (general tab) Domain name: ... Control Center -> Network --> (DNs tab) Search domains: ...
add some domain searches for DHCP sessions, e.g.
cd /etc/dhcp/ cp -pi dhclient.conf dhclient.conf.dist vi dhclient.conf prepend domain-search "example.com", "example.local";
change the resolvconf config directly
cd /etc/resolvconf/resolv.conf.d cp -pi base base.dist vi base search example.com
also make sure that the local system hostnames resolves itselfs as FQDN accordingly (it can point to
127.0.0.1 on a desktop)
In case you wanna keep the wrapper against dynamic name resolution AND search against your domain
vi /etc/systemd/resolved.conf Domains=DOMAIN.TLD