A-ha—trick question. You should be asking "Where's Up with the Title?"—only, you know, that question actually makes no sense.
It wouldn't have made sense to Emily Dickinson, either, because she never really went in for titles for her poems. It just wasn't her bag. But editors couldn't have just called every one of her 1,800 poems "Untitled," now could they?
What they did instead was to borrow the first line and use that as the title. They also added a number to the end of the title, to indicate—as best as they could determine—the chronological order of the poems she wrote.
In this poem's case, we have poem number 314, which… doesn't really tell us much of anything about what's to follow. The use of the first line, though, does set the stage for the remainder of the poem, and it does so by announcing the poem's central metaphor.
As a title, "'Hope' is the thing with feathers" lets us know that we're going to be talking about hope—as a concept, highlighted by quotation marks—and about a bird. In fact, we're going to be talking about these two things as one, and we're going to be doing that all poem long—where the hope-bird sits, what it sings, what might cause it to stop singing, etc.
Even though Dickinson didn't choose this for her title, and even though the editors picked the first line for the sake of convenience more than anything, we still say that this is a good choice as far as titles go. It sets the stage and gets us in the mindset for our encounter with the hope-bird in the lines that follow.