Upvote:4
You don’t really need a passport for a booking, and even if you add one, it doesn’t matter. There can be significant time between booking and flying and documents and requirements can change.
You need to present a passport at check in that needs to be valid for your current travel. Which one you present is up to you and United doesn’t care as long as it’s valid for travel.
I sometimes give them both and ask “which one do you want” as a joke.