What is the name of apoem that tells a story at times has characters?

Narrative poetry.

Explanation:

Narrative poetry is a type of poetry that tells the story of someone or something. It also sometimes has characters that speaks, the characters having their own voices within the poem.

Literary works such as "Beowulf", Homer's "The Illiad", "The Odyssey" or Chaucer's "The Canterbury Tales", the long poem "The Prelude" by William Wordsworth all come under the form of "Narrative Poetry". Though different in their own ways, they all have characterization, with some having conversations within them, along with a full story line. They tell stories but through verses, unlike a novel form. They have everything that a novel does, a story line, characters, plot, dialogues but the only difference is they are written and put forwarded in a verse form, unlike paragraph style of novels.