Thanks for your comments everybody. I did think of another possible solution - to have the rest of the Payne family "move away" (move them to the clipboard and delete them, or use MC to annihilate them), then take the original Payne family back to Build & Edit, change all of their names, save them again, and place them back in the same house. But I didn't really want to do that either.
As it turned out, I decided to start all over from the beginning. I got a bunch of stuck aging notices, and when I looked at the residents' tags in map view, I discovered several whose "days until birthday" were negative numbers, some of them over 100 days in the negative! I don't want to lose my residents to premature aging either, so I'm going to go through the resident population again, in the starter save for this game, and change the ages of any who are too far from where they should be. I'm glad I only played 2 days so far, so I haven't lost too much time.
@MidnightAura I've been playing for almost 7 years now, and this is only my third. Normally it wouldn't bother me to lose residents, since I don't play in rotation, and am therefore not nearly so attached to them as to my active families. But this time it's very different. I'm attached to them even though I'm not playing them, because I spent so much time making them and setting them up, and this is the first chance I've had to see how they will actually live their lives.