In reality, when large companies merge, it is rarely as simple as one taking over the other. Usually, there are complexities that cause strange mixtures. By way of anecdote, at one time I worked for a company that was perhaps #2 or #3 in its industry and which managed a fairly hostile takeover of a similarly-sized competitor. It was billed as a true merger, and the new company adopted a name chosen to signify this. In reality, much of the management of the acquired company ended up replacing equivalent managers in the acquirer; internal processes ended up a mishmash of systems previously in use at one or the other.

In the case of AA and US, I'd expect separate decisions regarding the name of the new company, the details of the new FF program, which alliance to stay in, which managers remain, etc. Just as an example, we could see the AA name, much of US' senior management, the AAdvantage name but details changed, and it could end up in whichever alliance makes sense for the resulting company (e.g., positioning relative to competitors and desired partners). In such a scenario, it wouldn't be accurate to say that either US or AA was "merged into" the other, even though one name or the other survives.