On the 15th of March 1985 the first internet domain name was registered: Symbolics.com
Symbolics was a computer manufacturer based in California, USA. They also made significant developments in software.
They produced what we would now term the first ‘workstation’.
Symbolics produced the Lisp machine and the L-machine (size of a fridge). These were fast changing times in computer and software development and by 1995 the Lisp series of machines was at an end.
The domain name is still registered and is therefore not only the first but the oldest.