A couple of sites I visited describe the naming of a product/service in some interesting ways. In one case, you can go for the direct route, where the name represents EXACTLY the product/service you are trying to describe. "PressPlay" as a name for a music service is an example.
The other route is a nonsensical name, with strong emphasis on recognition, pronunciation, and so on. For example, "Allegra" has nothing to do with the actual name of the medication, but since it is related to the word Allegro, which means to speed up, and Allegra is a sinus medication to alleviate sinus pressure, which makes people feel pretty darn slow, I can tell you... you get the point.
Marketers seem to be divided about the whole acronym thing. Some suggest avoiding it like the plague, other suggest that it can sometimes work.
I was thinking to suggest that JAG might be an interesting name. It is an acronym for Java API for Gaming, as LWJGL seems to be heading in that direction. That's just my off the top suggestion. Heck, you could use a fighter jet for the logo for it. Pick an F14 or an SR71, they're my favorites.