Im using Blender 2.78c and where I have seen in many tutorials people can select their graphics card in the User Preferences>System by clicking CUDA. I only have the option to click OpenCL and when I do it says only Hanain under it.
CUDA is used on Nvidia Cards. AMD Radeon cards use a different kind of hardware.
You can only use Open CL (and live with its limitations).
The Option "Hainan" is the correct and only option you have.
AMD cards appear in blender with the code name used for the GPUs architecture.
As an alternative you might want to try using other render engines other than Cycles, as explained in this post: Alternative Render engines can I use instead of Cycles for AMD Radeon GPUs?