This poem has a simple title: "Sympathy." On one level, this title indicates the "sympathy" that the speaker feels for the caged bird. He identifies with this bird and he feels its suffering. In this sense, the poem's title can be understood to reflect the speaker's own identification with the bird.
On a second level, we can understand the title of this poem as calling on us readers to have sympathy for both the bird and the speaker in the poem. By painting such a vivid picture of the bird's pain, the speaker wants us to sympathize with this bird, and with his own pain—which the bird embodies. What's more, if we know that Paul Laurence Dunbar was an African-American poet who was writing poetry at a time when African-Americans were in the midst of their struggle for civil rights, we can also understand the poem as asking us readers to sympathize with the plight of African-Americans as a whole. All in all, it's a pretty appropriate title, wouldn't you say?