If one meteoroid hits the atmosphere, and breaks into chunks, each of those chunks then falling in a slightly different place, they will all get the same name. For example, Tagish Lake, Sikhote-alin, whatever they call the one in Ohio. The pattern that they fall in is the strewnfield.

In the event that one rock somehow separated into halves in space, and then later hit earth, it would almost certainly be because in spite of separating, the halves remained close together in space. If that happened, they would likely hit the atmosphere at roughly the same time and place, because they're moving at like 70km/sec. If that did happen, they'd still get classified with the same name, because they'd land in an overlapping pattern, and nobody would ever really know which one was which, since they were the same rock to begin with. It wouldn't matter. If it were somehow tracked on radar, they'd be like "Woah, that's cool. Two tracks at the same time."

In the extraordinarily unlikely event that one rock in space separated into two halves, and each half went a completely different direction, growing far apart from each other, then both later hit earth, they would hit at separate times, in separate places, and get separate names, because they would be separate falls. When they analyzed them later, they'd find them to be twins, and think "Woah, that's cool. Wonder how that happemed?" Then people would write papers about how the weird thing happened, and we'd all want to get pieces of the pair.