"Whois" is a term that dates back to the early days of the Unix operating system and university networks. On Unix, the command "whois" searches to determine the identity of people on a remote server.
With the advent of the public Internet and DNS, the domain name system, the number of domain names and IP addresses allocated skyrocketed and the managing organizations, such as Network Solutions and ARIN published a publicly accessible database that mapped domain names to their owners.
In honor of the Unix command, the databases were titled whois databases and the act of looking up a piece of information from the database was called a whois query or a "Whois Search".