Mine's sorta long....
We live in Jacksonville and I have the First Coast News website as my homepage. One day I saw one of the reporters had a blog about the twins she was pregnant with. The blog was about how they couldn't decide on names and her husband kept picking stupid names. The Jaguars football team is big here, and he suggested naming the children Jacksonville and Jaguar (i guess he is really obsessed with the team) or Matt and Jones after his favorite player Matt Jones.
I was telling my boyfriend about this story one day and we started thinking about how Jackson would be a cute name for a son, and even Jax.
About two weeks later we got our Yorkie. He has so much spunk and personality I wanted a lively name. I also wanted something with only 3 letters. I thought Jax was a good fit, plus it has that sentimental aspect to it since this is where me and my boyfriend fell in love.

So I guess the name is short for Jacksonville.