Strange... I'm glad that XirenDThon asked the question, because I was too embarrassed to. I played Everquest up until after the Velious expansion release and just before the next expansion, whatever it was. During that time I frequented these boards, (same screen name), read the thick strategy guide from front to back and discussed the game with both my online and offline friends and never once heard it referred to as EQLive. When Everquest Online Adventures came out, I thought about playing, then finally caved and picked up the Frontiers version, just after it was released for my Sony Playstation 2. I started coming back to these boards again, luckily my account had not expired, and even then I never heard it referred to as EQLive. We always called it EQPC or EQ(PC). I'm not sure when Sony Online Entertaiment began officially calling it EQLive, but it was only within the past couple of months that I can recall first seeing it and wondering what it was. I assumed the people using the term were talking about the original Everquest, but wasn't a hundred percent sure, and didn't want to seem "out of the know" by asking; silly pride again. I can only infer that it is to further distinguish between the multiple "Everquest" games that are now on the market, including the original Everquest, Everquest Online Adventures, Champions of Norrath (an Everquest, Diablo like, game for PS2), and the soon to be released Everquest 2.
If any of the players who have been around for a lot longer than I, can remember when they first heard the term, it would be interesting to know.