inxi -G is one way to give info of your "card"
for me - old amd bobcat
Graphics: Card: Advanced Micro Devices [AMD/ATI] Wrestler [Radeon HD 6250]
Display Server: X.Org 1.17.3 driver: radeon Resolution: firstname.lastname@example.org
GLX Renderer: Gallium 0.4 on AMD PALM (DRM 2.43.0, LLVM 3.7.1) GLX Version: 3.0 Mesa 11.1.1
Update for Sid just happened libdrm-radeon1:amd64 libdrm-amdgpu1:amd64 should be to testing in maybe 5 days. I ride with radeon be sure you have contrib and non-free in your debian source. https://wiki.debian.org/AtiHowTo
A few years ago, I was using catalyst, but - pita. Catalyst has diverged from the newer xorg at times. radeon is much simpler and works well with new kernels.
And for fun, you can install radeontop to see if any processes are clogging your pipes.