ATI as a brand will still exist. I'd think the ATI logo would be there (if any).
The merger is beneficial for ATI because they will now have their own fabrication capabilities. Before it was always done externally. Now they can do it themselves, and do it better because AMD's process is more advanced. AMD also works with IBM on fabrication, and IBM kicks ass on that front.
And it's beneficial for AMD because they'll be able to create IC's that contain the GPU on the chip. The "system on a chip" concept has been talked about for a long time, and this is another step closer to that. It'd be benecifial for would-be console systems, video ipod-like devices, PDAs, small form factor computers, and basically any media-related device.
Of course, for computer OEMs there will likely be a discount if they use AMD CPUs and GPUs.
I don't think we're going to see a shut out of options unless Intel decides not to grant AMD/ATI a license to their platform. But AMD's not in a position where they can make demands. AMD seems to be going in the opposite direction. Their "Torrenza" platform is an open architecture that opens up some new possibilities, for one.