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But the English name for the constellation is "Capricorn"...
All the constellation names are Latin. ;) Capricorn is a variant of Capricornus, and I think that in such cases we should follow the International Astronomical Union, even though every now and then its form is less common (the other being Scorpius).
Look it up in a dictionary. The IAU, as I understand it, gives the names of the constellations in Latin, which is perfectly understandable. But we're using English here, not Latin. See, for example, these pages:
As said, all the constellation names - both versions - are Latin or some slight alteration thereof. In some cases the IAU form is in fact not the original Latin (Scorpius vs Scorpio). Nonetheless they are supposed to be the official versions, for any language, and if you pick up most astronomy texts or star atlases Capricornus is what you will find marked. The dictionary has never been particularly interested in naming all the constellations (you won't find Lacerta) and is giving a form more common thanks to its use in astrology, which has never been that interested in accuracy anyways. Your choice, but I would again suggest that we follow the literature.
It would be a shame to segregate the zodiac from the rest of the constellations. Other than Cancer, I think the only constellations that will collide are those with heroes for namesakes, and that isn't too bad. And don't we think something like Ursa Major deserves a top level page?