As for what to call this piece in English, I don't think there is really an established name sanctioned by academic opinion. One option is certainly to stick with the name used in Wikipedia, "Biche of Balazote", which occurs in a number of places, some of which Taña has cited (and many or most of which could well be derived from the Wikipedia page).

As an alternative, I am quite attracted to "Beast of Balazote", which is what Carlos Fuentes calls it in The Buried Mirror: Reflections on Spain and the New World (p. 19), based on his BBC TV series (the phrase may have been coined by a translator):
http://books.google.es/books?id=Yyj5PK-15UwC&pg=PA19&lpg=PA1...

The figure is in fact a bull with the head of a man. In an unsigned article "Pre-Roman Antiquities of Spain", published in 1907 in the American Journal of Archaeology, 11: 182-93, it is illustrated with the caption "Bull with Human Head from Balazote" (p. 187).
http://www.jstor.org/stable/496934?seq=6

So perhaps you could call it the "Bull of Balazote", though I don't know whether anyone has. Or possibly "Bull-Man of Balazote"; the bull-man often has a bull's head on a man's body, like the minotaur, but here's an Old Babylonian bull-man in the British Museum with a human head (albeit apparently with horns originally).
http://www.britishmuseum.org/explore/highlights/highlight_ob...

Anyway, there are several possibilities. One reason for leaving it as Biche or indeed Bicha is familiarity.

But as for what "bicha" means here, the dictionary definitions are quite irrelevant. "Bicha" has none of its normal meanings: the devil, a snake, or a decorative figure of a woman with the lower body of a fish (see DRAE). In this case, as the Wikipedia page explains, is simply a calque of the French word "biche", meaning doe (female deer), because the French archaeologists who first worked on it thought the body was that of a doe (which seems odd, but there we are) and named it "La Biche de Balazote". It's certainly not a caryatid.

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Note added at 2 hrs (2013-05-10 00:56:51 GMT)
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Personally I think it's more suitable to call it "the Beast/Biche of Balazote" rather than "the Balazote Beast/Biche", just as, for example, we call the Dama de Elche "the Lady of Elche", not "the Elche Lady".

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Note added at 2 hrs (2013-05-10 01:03:09 GMT)
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I am very sceptical about the definition in El País of "Figura ornamental característica del arte ibérico, en forma de animal o mixta, con una parte humana y otra animal". It seems to me that this is quite probably derived from the name of this piece, which is only called "bicha" because of a mistake. I don't this "bicha" means that in a general sense.

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Note added at 2 hrs (2013-05-10 01:39:20 GMT)
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In other words, if you wanted a literal translation of the actual meaning of "bicha" here, it would be "The Doe of Balazote". But it would be absurd to call it that, since it is not in fact a doe at all.

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Note added at 6 days (2013-05-16 15:05:13 GMT) Post-grading
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I didn't have time to answer your note earlier, and I see from your discussion commenta that you have found an eighteenth-century reference showing that bicha did once mean a hybrid.

This turns out to be very interesting. First of all, let's be clear that, as you say, the correct word for a creature like this is a hybrid, not zoomorph. A zoomorph is a representation of a human being or a god in the form of an animal. A hybrid is a combination of different species (either human-animal or animal-animal).

Well now, it turns out that the English definition you found from 1786 reflects the main definition of "bicho, o bicha" in the first RAE dictionary (known as the Diccionario de autoridades, this volume of which appeared in 1726:

"Ciertas figúras de hombres, ù de béstias, que se remátan de medio cuerpo abaxo, quando se fingen entéras en otra forma de la que tuvieron al principio: como en follages, peces, ò algun otro animál, segun la idéa que mejor, ò mas proporcionada paréce al Pintór, ò Escultór, para mayor adorno de los lugáres en que los empléa [...]"

This is a particular kind of hybrid: top half human, bottom half foliage, fish "or another animal", and for particular decorative purposes.

Anyway, by the time the RAE published its next dictionary in 1770, this definition had disappeared. "Bicho, o bicha" simply meant "Qualquiera sabandija como lagartija, alacran, &c. Hoy solo se dice bicho".

And so things remained in subsequent editions up to 1884 inclusive. But in 1899 the RAE reintroduced a definition rather similar, though narrower, than that of 1726, and as an architectural term:

"Arq. Figura de animal fantástico, que entre frutas y follajes se emplea como objeto de ornamentación, principalmente en la arquitectura plateresca, para llenar frisas y netos de pilastras".

This was left unchanged in the 1914 edition, but in 1925 it was modified to read as follows:

"Figura fantástica, en forma de mujer de medio cuerpo arriba y de pez u otro animal en la parte inferior, que entre frutas y follajes se emplea como objeto de ornamentación"

And this definition appears in all subsequent editions of the DRAE up to and including the present.

So "bicha" did indeed mean a hybrid, though only a certain kind of hybrid, in the early eighteenth century, though by 1770 the Academy apparently considered that this definition did not warrant inclusion.

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Note added at 6 days (2013-05-16 15:06:10 GMT) Post-grading
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By the way, I have consulted these dictionaries through the RAE's extremely useful NTLLE portal:

http://ntlle.rae.es/ntlle/SrvltGUISalirNtlle