Good Old Games turning to GOG is the equivalent of the Sci-Fi channel turning to "SyFy", which basically meant they wanted to broaden their horizons and bring in more viewers for a variety of shows. That's also when reality TV and wrestlling appeared on TV spots that once had grand sci-fi shows. In much the same way GOG has broadened their horizons to encompass not just classics, but newer games as well. At it's core though, SyFy still means sci-fi, and GOG still means good old games, even if it's open to a broader perspective.
On the SyFy note, I never really got the name change, and apparently from what I've been reading they haven't had many viewers on their channel ever since they changed the name and how they run the network, ever since the newer Battlestar Galactica got cancelled. They want to harken back to the days of grand sci-fi shows, and they want to get back into space as well, and cut down a bit on their cheesy movies.
GOG's not in that same boat and it's of course a different industry, but the concept is the same; change your name so you can broaden your foundation. Just as long as you don't destroy what you were built upon, you adhere to your values and that's what matters the most.