A simple name-change would not indicate to me a need for a new gamepage. Moving to a new engine might, however.
In the case of making a new gamepage, the thought in my head is to flag this gamepage as "canceled", and redirect players to the new gamepage. As for this gamepage, and the downloads you have associated with it, my initial response would be to retain them. Like, I've only ever taken down one download ever, and that was for a game that was supposed to be a collection of abandoned games... that I ended up making anyway :P