Hi MrsRobinson,
There's no actual 'end' to the game as such. Many people have had games running for years. There are awards for various achievements and so I suppose if someone were to get all the awards they could think of that as a an object to achieve (or at least get as many as possible). Some events give hints of an interesting history to the house, but they're really for 'flavour' and aren't part of a puzzle. Maybe some of the questions raised in those events will be answered in VF3!
Usually, after a lot of generations, the peeps have earned an enormous amount of cash, and I think a lot of players will restart the game at that point to set themselves a proper challenge.
The peeps' names can only be changed in the desktop/laptop (Mac/PC) versions. They can't be changed on iOS or Android.