I have a laptop with a similar problem. It's a samsung with A6 APU and Radeon HD 6470M GPU (dual graphics) and when I bought it the graphics card was detected as Radeon HD 6470M. After installing the beta drivers (one by one as they were released), Windows started "seeing" my GPU as "Radeon HD 6400M series" which is good. Then, at 13.12 version, my GPU suddenly became "Radeon HD 7400M series", just like you.
It was a driver issue, however my computer was working fine, even in games (I had the regular 'this-game-does-not-support-dual-graphics-and-catalyst-doesn't-know-I-have-a-game-running-so-I'm-stuck-with-the-dedicated-gpu-lagging', but it was working without saying anything).
Obviously it's a driver issue and reinstalling Windows (preferably the version (7, 8, 8.1 etc.) the laptop came with) and installing the drivers from the laptop manufacturer's website, you won't have any problems. If the problem consists, report it to the manufacturer, but first make sure you haven't downloaded the wrong driver (like for an other laptop). If you want, you can try the latest beta version that AMD offers, but I don't know, even with the latest version, I still magically have 7400M series graphics card.
Given that the driver is one pack for too many graphics cards, they even have desktop and laptop gpus together, I GUESS that since your computer "thinks" you have 7400M series GPU, so did the installer. So I wouldn't recommend using a driver that was probably tested on some other GPU.
Hope I helped...