The full title is "Proem: To Brooklyn Bridge." This poem is the first of eight sections of Hart Crane's book The Bridge. "Proem" is an archaic word for "Prologue." Crane might have been interested in the rhyme with "poem." Like the "Prologue" from Chaucer's Canterbury Tales, the "Proem" introduces some of the central themes and ideas of the book, like the alienation of modern life and the potential for redemption and unity.
Many people ditch the "Proem" part and simply refer to the poem as "To Brooklyn Bridge." When you address a poem "To" something, you are usually in the land of the ode, a kind of Greek poem that became popular again among 19th century British Romantics. (Think of Keats' "Ode on a Grecian Urn" or "To Autumn.") The poem is quite literally addressed – using the second person – to Brooklyn Bridge. For more about the ode form, check out "Rhyme, Form, and Meter."