If you want to be able to search multiple domain names on a desktop that uses DHCP then you need to make sure those domain names get added to /etc/resolv.conf. The way to do that is to add the DHCP option domain-search specifying the list of domain names to /etc/dhcp/dhcpd.conf:
option domain-search code 119 = string;
option domain-search "domain1.com", "domain2.com", "subdomain.domain3.com";
Please note that the search list is limited to six domains with a total of 256 characters.