I really have no idea either, but there can be two reservations but still only one stay. This happens to me when I have a personal night followed by a business night. I'll have two reservations, but one stay. I've never had to change rooms (at a Marriott, but yes at another chain) but I'm only supposed to get a single Welcome Gift. Sometimes I get the second Welcome Gift, but by the rules I shouldn't. In your instance, the two of you are arriving once and staying two nights. Let's face it: The second reservation and swapping names is totally to game the system, which they will know.

My guess is if you called and asked the hotel, they would say it's one stay, so you probably won't want to do that. If you show up with two reservations and appear to be trying to pull one over on the hotel, they probably won't like that. Again, if these are small and of little cost to the hotel, you shouldn't have a problem, but if these are costly, you might. Again, while I don't know the ultimate result, if the hotel argues the point you wouldn't have much ground to stand on. Even if you say you are doing it so you each get some credit for the stay, it still fits within the definition of a single stay.