The poet-speaker
The speaker of the poem is both its major "character" and, in some sense, its "setting," as the poem is best understood as an exploration of the speaker's own consciousness.
The mourners
The only other person-like figures that appear in the poem. The speaker never actually sees the mourners, never individuates or describes them, and they have no "backstory" to speak of. She merely hears them going about the business of mourning at the titular funeral.