https://en.wikipedia.org/wiki/Search_domain

Your DHCP/SLAAC RA tells clients "here is a list of search domains, when you attempt to query a bare name, also look for the name plus any suffixes listed in the search domain list". So on a system with "home.arpa" in the search domains, you can do something like 'ping myhost' and your system should attempt to resolve 'myhost.home.arpa'.