Though it begins on a bridge, musing about the night sky, the poem quickly reveals its main subject: the nightingale, a bird known for its melancholy song. John Milton, with whose work Coleridge would certainly have been familiar, frequently referenced the bird, calling it "melancholy."
In fact, the bird's reputation is why it was chosen. With an overall argument against using nature to reflect back one's own emotions, a familiar poetic subject like a nightingale would help drive the message home.
And though the poem frequently returns to topics like youth, the moon, and the beauty of nature, it all circles back to that nightingale and how our emotions affect the way we characterize that little bird and its song.
All in all, it's a pretty appropriate (and literal) title, there, Mr. Coleridge.