Journey of the Magi
On one level, the speaker here is mega-obvious. The "I" in the poem is very clearly set up as a Magus, one of the three kings making the long trek to Bethlehem to offer gifts to the baby Jesus. We can almost see this particular speaker as a grandfather-type, hanging out by a fire, telling someone this story that, at the outset, looks awfully like the ol' "having to walk ten miles to school uphill both ways in the snow" story.
Of course, this tale is decidedly more somber, and towards the end, when the point is really reinforced that the narrator is speaking about the long ago and far away, the Magus's tone moves from mere storytelling to almost painful misery and melancholy.
But throughout the poem, it also seems like there's someone other than the Magus at work. If that sounds a little creepy, that's because it is. The words that come out of the Magus's mouth are almost too symbolically perfect, too ESP-like to really be his own. If we dig deep into the way in which the Magus's story is constructed, we stumble upon a ghost-speaker in the poem, who's wielding all that symbolic mumbo jumbo with the utmost care.
So even though Eliot's writing a dramatic monologue here, he's not concealing himself very well in the persona. His incredible well-read-ness shines through all the time, putting words in the Magus's mouth that are symbolic of things and events that the Magus couldn't possibly know—the trial and death of Christ, the Lancelot Andrewes sermon, bits of the New Testament, and Shakespeare. So, although the speaker might walk like a Magus, he only half-talks like one. The other half is all super-bookish Eliot, a careful puppeteer.