In the early days Ken used to hand-cut Unix distribution tapes, often with a note that read "Love, ken". Old-timers still use his first name (sometimes uncapitalised, because it's a login name and mail address) in third-person reference; it is widely understood (on Usenet in particular) that without a last name "Ken" refers only to Ken Thompson. Similarly, Dennis without last name means Dennis Ritchie (and he is often known as dmr).
Ken was first hired to work on the Multics project, which was a huge production with many people working on it. Multics was supposed to support hundreds of on-line logins but could barely handle three.
In 1969, when Bell Labs withdrew from the project, Ken got fed up with Multics and went off to write his own operating system. People said "well, if zillions of people wrote Multics, then an OS written by one guy must be Unix!". There was some joking about eunichs as well.
Ken's wife Bonnie and son Corey (then 18 months old) went to visit family in San Diego. Ken spent one week each on the kernel, file system, etc., and finished UNIX in one month along with developing SPACEWAR (or was it "Space Travel"?).