Given the presentation of the legendaries of higher importance, from just about any generation, I find it highly unlikely that there are multiple. I think that, based on various elements within the games and the anime, it's reasonable to assume that some of the legendary trios and duos have multiple iterations throughout their regions and the Pokemon world. However, none of those that are depicted as being deified to any extent - the Sinnoh box trio, Arceus, Hoenn box trio, all Alolan legends, Kalos box duo - or any of the other very powerful examples like Ho-oh, Lugia, Mewtwo etc. have ever been depicted as being multiple in nature, or even hinted. Granted, you could argue that their availability in multiple regions counts, or that any of the Creation trio being born from an egg in the Sinjoh Ruins might count, but the Alolan legends obviously don't have an opportunity for that kind of availability yet.
Regardless, I agree with someone above noting that Game Freak probably doesn't care much about the implications of catching a deity, and that there's no real sign that being captured inhibits their ability to carry out their duties provided they have a "good" trainer (as all protagonists generally are). If you catch Tapu Koko and some stuff happens to go down it can probably willfully escape it's ball or signal to you "yo, stuff's going down, let's get to my island bruh." I imagine that the relationship between a trainer and a legendary is more like a complex social contract than a regular capture.