When talking about something, where do we place its name in the sentence?

I agree that the first example sounds the most natural. However, I believe that this is due to some conflation of appositive nouns and genuine adjectives.

In the first two sentences, "Eclipse" functions adjectivally as a noun (restrictively) in apposition to "The development environment". Typically, a restrictive appositive follows the noun it restricts (and so your second example is most correct, in some sense. However, the adjectival sense is so strong, and English favors adjective-before-noun word ordering to such a degree that the first example does sound better.

In the third example, "Eclipse" is the subject of the sentence with "the develop environment" functioning as a non-restrictive appositive. As such, it is truly parallel to you "John the intern" example. I'd say that it sounds less natural because it omits an actual adjective to emphasize the adjectival nature of the phrase. For instance, "Eclipse, the most popular development environment," sounds just like "John, the new intern,".