When we talk about the first domain being registered, we think of .COM or .NET don't we, but there's been domains around longer than that - for example ARPA (the original defence network protocol - it STILL exists as a reverse lookup domain!).
Run a WHOIS at NetSol on 'ARPA' and have a look at the record.
You can also WHOIS complete country TLDs like UK and NU etc.
So whatever the first .COM name was registered wasn't technically the first name. But we do think of registered as being paying a sum for a year's (or more) worth of renting a domain. You don't really only your domain - you can only 'rent' it for as long as you have paid for. (Hence Cybersquatters got their name on unpaid registration snappers).
Some early domains:
Domain Name: THINK.COM
[....snipped....]
Record last updated on 20-Mar-2002.
Record expires on 23-May-2005.
Record Created on 24-May-1985.
Domain Name: SYMBOLICS.COM
[...snipped...]
Record expires on 16-Mar-2007.
Record created on 15-Mar-1985.
Domain Name: IBM.COM
[...snipped...]
Record expires on 20-Mar-2005.
Record created on 19-Mar-1986.
Curiously, Microsoft only got their domain in 1991!
AOL got theirs (aol.net first) in 1992!
Some of the earliest names were EDU names for many of the main computer-connected university.
It's a shame we can't get access to the whole of Network Solutions' WHOIS database - I bet there are some real gems lurking in there!
Though you can access the root files at versign-grs.com but you have to be vetted and have a static IP address...