I don't see this happening at all...
First, there's no way that United would drop their own name. They're so recognized (good or bad) that doing so would be nothing short of suicidal.
Second, when the merger is approved, I would be surprised to see the integration of the two airlines take so long. It's well-known that United has a livery/image update in the works -- they've said so themselves. It's a great time to release the rest of the new image.
What I predict will happen is that right away, signage will be changed at all major stations to show the new name as United/US Airways or something similar. Then, as operations are integrated, US Airways disappears.
It may take 2 years to get all the signs updated, all the planes repainted, all the new marketing collateral out, etc., but I don't think that US Airways would exist as it does today as some sort of quasi-independent carrier.
(PS - I choose my words carefully: when the merger goes through. DCA-ROCguy and I have gone rounds and rounds on this one before, and while I don't want to start that war again, this discussion topic is far from moot.)