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The first domain name was Symbolics.com, registered by Cambridge, Massachusetts computer company Symbolics Inc. In addition to being the oldest domain name, it's also the longest running and you can still visit it today, though it's no longer under operation by its original owners, who sold the domain in 2009 after 25 years of ownership.
Today Symbolics.com is owned by private digital investment firm XF.com, which bought the domain for an undisclosed amount, presumably as a means of marketing its services, though there is a certainly a cool factor in owning the Web's first domain name.
Symbolics Inc. was a spinoff from the MIT AI Lab and engineered/manufactured a line of Lisp machines (designed to run software coded with the Lisp programming language) which were the first commercially available general-purpose workstations.