The origin of the term is contested, but may be derived from "George Stick", named for a possible inventor.
I knew the device itself predated gaming, but I always assumed it gained the joystick name from some game company. I'm surprised to to learn its unrelated!
It's company policy never to imply ownership in the event of a joystick... always use the indefinite article 'a' joystick was found in your luggage. Neveryour joystick
Yeah, it's bogus. This is some speculation that someone put in Wikipedia but there's no published source. It's just a folk etymology that some enthusiast thought was endearing. Not a single reputable source will substantiate this, like most folk etymologies.
The more plausible explanation is that joystick comes from the aviation parlance and was originally ribald sexual innuendo (those flyboys did need to blow off steam), with the “George Stick” explanation being invented after the fact to come up with a plausible clean etymology.
I always assumed it was "joy" because games are fun, And it's a stick design for playing video games so Joy. Stick. Joystick. But I've apparently assumed wrongly.