Lots of thought goes into naming things, especially restaurants. Naming things are a pain in the ass. With a hot dog joint, It was really easy to get too cute and the next thing you know, you wind up with "Uncle Wiener's Big Dog House...Home of "Fido" the Foot Long" or something awful like that.
What we were trying to do was to formalize the process and exhaust every option, good or bad. We had a few rules: No dog references, no references to the male genitalia, and no baseball references. Everything else was fair game. As you can see, some of us couldn't help "going there." In the end, we ended up where we began.
We wanted something catchy, with two repeating one syllable sounds that were consonants - which is why the working title of the project was JJ's to begin with.
Coincidentally, there are a lot of "J's" in my family. Me, my dad and my kids' names, for example. So there is a personal connection of sorts. Really, we just wanted the place to be easy to remember.