For another option, I fill 1 January, for New Year + First domain created in the world Nordu.net. But 15 March is also good day since first domain can be registered to public is Symbolics.com on March 15, 1985
Answer: The first domain name registered was Symbolics.com. It was registered March 15, 1985, to Symbolics Inc., a computer systems company in Cambridge, Mass.
It was not the first domain name created, however — that title goes to Nordu.net, a Scandinavian research collaboration, which created the domain Jan. 1, 1985. Nordu.net was used for the first root server (nic.nordu.net), according to DomainNameNews. However, once registration was permitted, Symbolics got in the door first.
As a bit of fun (considering we're an investors forum), I'd go with the first commercial domain, being Symbolics (15th March). Otherwise, if its specifically domainer kindness and respect day, we make it @Bob Hawkes birthday