Microsoft has been pushing the Bing name over Live Search for awhile now so this oversight is kind of interesting. DavidB was poking around on the old Live Search download page (m.live.com/download/) and now it redirects to Bing (m.bing.com/download/).
On that page you can see that the Windows Mobile app has been renamed to Bing for Windows Mobile but the BlackBerry app is still called Live Search for BlackBerry. Microsoft is a huge company with untold resources that this oversight is kind of interesting. Its also sad to see that they have not updated the app for the Tour since if you install the 4.7 version it expects a touchscreen.
Still maybe some discussion will prompt Microsoft to update the app… It is a pretty good app with some more category specific functions compared to the Google Search app.