Difference between DHCP options 'Domain-Name' and 'Domain-Search'
The domain-name option specifies the client's domain name (of which there can only be one), and is specified in resolv.conf with the domain keyword. This is the domain which will be used when running hostname -f on the client.
The domain-search option specifies a list of domains to use when looking up bare hostnames, and is specified in resolv.conf with the search keyword. If this option isn't provided it defaults to the single domain provided by domain-name.