Weyer gives this spirit as Caim and also as Camio, and the Lemegeton manuscripts vary between Caim, Caym and Camio. The resemblance to Cain, the first murderer of Genesis, is obvious, frequently asserted, and considerably weaker than it looks.
The difficulty is Camio. If the earliest recoverable form of the name is Camio, then Caim is a shortened or corrupted variant and the resemblance to Cain is an accident of the corruption, which would mean the derivation runs backwards from a copyist's slip. If Caim is earliest and Camio the elaboration, the case improves. The manuscripts do not settle which came first, and both forms are present in the sixteenth-century material.
There is also a problem of fit. The Goetia's Caim appears first as a thrush and then as a man with a sharp sword, answers out of burning ashes, and grants the understanding of the voices of birds, of cattle, of dogs and of the sound of waters. Cain, in Genesis, is a farmer, a murderer, a marked exile and the founder of a city. There is no bird, no divination and no augury anywhere in his story.
The offices, by contrast, have a very clear background elsewhere. Understanding the speech of birds is a widespread motif, it is what Solomon is granted in the Qur'an, it belongs to Siegfried in the Norse material, and augury from birds was a formal Roman priestly discipline. That is where this entry's content comes from, whatever the name turns out to be.
Which is the general lesson of the Goetia's etymologies: name and content usually have separate histories, and matching them is a modern habit rather than a textual fact.