Anne Killigrew
She is the subject of the poem and was real life individual that Dryden based this poem upon. Dryden notes her for her beauty and intellect, as she was a famed poet herself. The poem entails his admiration for her wit and her morals. He particularly drew attention to her morals and the correctness of the way she upheld them.
John Dryden/Narrator
The author himself is referring to her as a fellow poet and to how much she has accomplished. He clearly has great respect and admiration for what she achieved, as well as being able to observe the physical beauty that came with her intellect. He is speaking the poem as an elegy, an ode to her and her career.