To make my meaning more clear, I visited ancient Corinth today and the museum was absolutely full of headless statues and bodiless heads. To me, all these toga wearing bodies looked very similar, yet the museum had them labeled as statue of Dionysus, Augustus, etc. Similarly, it seemed Gods and politicians could be recognised just from a statues head, even if the God had no real distinguishing features, such as Aphrodite. So my real question; how can archeologists tell a headless statue in a toga is Zeus, or that a disembodied female head is Artemis rather than any other God? Thanks for any answers.
First, these sorts of identifications are not always dependable. Depending on the institution/author, an informed guess might be passed off as a confirmed ID. That happens a lot unfortunately.
But the process of identifying ancient works can, in general, be productive if enough information is available. Epigraphic evidence might be present on or near the work (though inscriptions often record info about the patron, not the piece itself). Maybe there are certain symbols or motifs associated with one subject or another. Maybe the artwork just resembles another confirmed piece whose subject is known. Copies weren't uncommon in the Greek and Roman worlds, so even fragments can be matched up with a sister piece. Perhaps the building in which the work was located gives clues: for example, one would expect to find a grand sculpture of Jupiter in a Roman temple of Jupiter. That can lead to a sort of chicken and egg problem if the temple hasn't been ID'd with certainty (if the temple is identified by the statues, and the statues are identified by the temple).
In the forum of ancient Pompeii, there's a large building called the "Building of Eumachia" which is poorly understood. Inside there's a statue of the patron, identified by an inscription. Outside, in the courtyard space, are three semi-circular statuary niches without any useful inscriptions. In 1820, the excavators found "the upper part of a cornucopia, the foot of a life-sized statue, and an inscribed herm" (Dobbins 1994, 652). So there's not a lot to go on here in terms of making an ID for what the statues were.
But Richardson has suggested that one of the statues in the central niche was of Concordia, in part because the architecture of the building corresponds to that of a near-contemporary shrine to Concordia Augusta in Rome. On this evidence, he even suggests there was a (now missing) statue of Livia in the central apse. Basically the idea is that Eumachia may have patronized the building to associate herself with the Imperial cult. There's no other statuary in the building that served this role, and these apses are very prominent at the end of the courtyard. There's a lot more detail to go into there, but my point is that in this case, historians have made a reasonably believable ID on the basis of only a few fragments of a statuary group.