Whatever name or acronym we put on them, there are a few functional categories of kit.
First, there is what you carry on your body at all times. You don't leave it in the car, so it's usually in pockets or on a belt, but some people use a small man-purse. Whatever you choose to carry it in, this is what we usually mean by "EDC."
Then, there is a bag you have with you whenever you leave home, but not necessarily on your body. This could be a small backpack, or a shoulder bag. Whatever it is, this is the bag you have to get you FROM wherever you happen to be, TO home. You can leave it in the trunk of your car in case you break down, leave it in your office when you're at work, whatever. This is what we mean by a "GHB." Obviously you could use it to go somewhere other than home, if home is not an option.
Lastly, you've got a kit you keep at home, in case you evacuate from there. This is the largest of your kits, and is what many people call a BOB. Some people specify whether it's a 72 hour bag (for a short-term evacuation), or an INCH (I'm Never Coming Home) kit.
This may all seem obvious but it wasn't always obvious to me. So, it sounds to me like your JOE concept is basically just a variant of the GHB: you carry it with you, wherever you go, but may leave it in the office or trunk of the car rather than physically on your body at all times. I do see a sort of difference, though, in that you're thinking of it as a go-away-from-there rather than get-home-from-there kit, so I can see why you want to call it by a different name, to reflect this difference of intent. If calling it a JOE makes more sense to you, go for it.
Now, here's my caveat: unless you're going to carry two bags everywhere, one to get your home and one to run away with, whatever bag you're carrying needs to be adaptable to either possibility. If your neighborhood catches on fire, your "Get Home Bag" may become a de-facto JOE, whereas if there is some kind of plague or something, you may need to use your JOE to Get Home so you can shelter in place.
So, really, BOTH names are flawed. But GHB has priority (in that it's been in use longer), so we can either stick with it, or try to introduce a new standard, with predictable results.http://xkcd.com/927/