I think there is an example in Europe. myTaxi has been rebranded to FREE NOW. The change has been dictated to free the brand from just the taxi business connection. But I believe it was unfortunate, at least for their taxi business. I don't have hard numbers, but the new name and logo seems to be random, completely unrelated to taxis, so when you see a car with it, you have no idea that the driver is a taxi driver. It's 2 years now with new name, but they iOS app is still named: FREE NOW (mytaxi). Me and my friends always have to ask someone "how mytaxi is called now?" because the app is no longer under M in the phone.
Worse for the company is that, since myTaxi was extremely catchy, there came a competitor called iTaxi, and many believe it might had take over some of the clients just because people trying to find myTaxi installed iTaxi instead, as FREE NOW looked cryptic and unrelated to taxis for them.