If you have yet to see the first episode of Disney’s Loki series, this essay contains spoilers. This episode lays out some of the key metaphysics of the MCU: there were numerous timeline branches (alternate realities) that engaged in war with each other. This was addressed by the Time Keepers pruning all the branches until only one timeline remained. To ensure that the timeline does not split, the TVA (time cops) exists to police problems. Among these problems are variants; people who somehow deviate from the sacred time stream.
Loki is, obviously, the main character of Loki. In fact, he is two main characters: the anti-hero Loki and the hero-anti Loki (the villain). Since the metaphysics of the MCU allows for time travel, this entails that the same person can be at different places at the same time. They can, for example, even fight. While this is a metaphysical mess, this means that time travel can be used as a multiplier: a person can time it right so that different versions of themselves all arrive at the same place at the same time. So, for example, Loki could show up to fight an enemy at a set time and arrange for himself to go back or forwards in time ten times and end up with eleven of himself to overwhelm the foe. This, of course, leads to the usual paradoxes and problems. A future Loki could tell a distant past Loki about things that a middle past Loki did not know, but then the middle past Loki would know it. While this is even more of a mess, the time travelling Lokis could remain there in that time and start their own lives or perhaps travel back to a more distant past over and over to create a vast army of Lokis that meet up at a future time to do whatever it is that his character arc directs him to do.
Such time travel has various other problems. One common point brought up in time travel tales is the importance of not changing the past. Some sci-fi stories do allow a change in the past to somehow change the future, other stories simply make it so that whatever the time travelers do is what happened anyway—that is, they make no change in the past because what they do is what they did and will always done did. The classic grandfather paradox falls into this family of problems: if a person goes back to the past and changes things that impact their ability to go to the past (such as killing their grandfather), then they could not go back to change the past and hence the past would be unchanged and so they could go back to the past. But they could not, because if they made that change then they could not go back. And so on. In fiction, the writers simply write whatever they wish—but this does not address the matter of how this would all really work.
There is also the problem of personal identity: in the metaphysics of the MCU (assuming this is not all a deception in the show) there is one sacred timeline, so variants arise from this timeline. While a new timeline branch could presumably also spawn variants that create additional branches, I will stick with the sacred timeline as the basis of discussion.
If there are two Lokis in the show, then they presumably both spawned off the main timeline. Perhaps one Loki “divided”, or one Loki “split” from the other Loki. Or perhaps there are three (or more) Lokis: there is the Loki who remained on the sacred timeline and was killed by Thanos. There is the Loki who escaped from the Avengers because of their time heist (the anti-hero of the show) and the third Loki who is the villain. Because of time travel, the third Loki might have split from the second Loki in the future. Also because of time travel, maybe the villain Loki is the hero Loki of the future. As always, time travel is a mess.
Having multiple Lokis does create the usual problems for personal identity. After all, what provides personal identity is supposed to make a person the person they are, distinct from all other things. As such, it would seem to be something that should not be able to be duplicated—otherwise it would not be what makes an entity distinct from all other things. After all, if there are two Lokis in a room, there must be something that makes them two rather than one. There must also be something that makes each of them the Loki they are. But is this true?
One approach is taking the lead from David Hume when he writes about personal identity. After he argues at length that a person is a bundle of perceptions, he ends up saying that, “The whole of this doctrine leads us to a conclusion, which is of great importance in the present affair, viz. that all the nice and subtle questions concerning personal identity can never possibly be decided, and are to be regarded rather as grammatical than as philosophical difficulties.” While this might be true, it does not satisfy.
Another approach is trying to sort out the metaphysics of personal identity in the context of time travel. After all, time travel requires that entities can be multiply located while personal identity would seem to forbid duplication of what individuates. The reason time travel requires multiple location is that something from one time travels to another time and the matter or energy that makes up what travels will also be present when it arrives. So the same thing will be in two places at the same time; something that is not normally possible. But one could accept the existence of metaphysical entities that allow this.
Yet another approach, and one that seems to match how the timelines are presented in the show, is that a branching creates an entire new reality that is similar but not identical to the first. This would also duplicate the people, perhaps creating them ex nihilo. So, the various Lokis would be similar people, but not the same person.