The main title of this poem is just plain "Kubla Khan." It's a pretty great name, isn't it? Sounds tough, mysterious, and exotic. We're willing to bet that Coleridge wanted that name to echo in a big way, to call up associations and feelings. It sets a tone for the poem, since the title transports us to another place and time before we even get started. But there's another piece. The full title is: "Kubla Khan Or a Vision in a Dream. A Fragment."
All of a sudden, Coleridge is giving us a much more detailed description of the poem itself. The famous back-story, (as told by Coleridge), is that he wasn't feeling well one night. So he took some opium (a drug), and had this strange dream. We think this really explains a lot about this poem. Do you feel how hard he works to describe an altered state? The meter, the rhyme the subject matter are all trying to make you feel what it's like to see things that aren't normally there. Letting you know that it's not only a dream but also "a vision in a dream" leaves you extra prepared for the weirdness that's coming.
Last of all, how about "A Fragment?" Apparently Coleridge dreamed about writing several hundred lines, and when he woke up, he started writing them down. He was interrupted, in the middle of writing, and when he came back, he had forgotten the rest. What about this poem might make it seem like a fragment? Does it seem finished to you?