A narrative poem that tells a story through dialogue and action is called-

Ballad is a narrative poem that tells a story through dialogue and action.
A lyric poem of fourteen iambic pentameter lines is called sonnet.
Ode is an exalted lyric poem that begins with an address to someone, instil anguish in the middle part and ends with consolation.
Dramatic Monologue is a kind of lyric poem in which a single speaker expresses his thoughts and feelings to a silent listener.
Source: An ABC of English Literature, Dr. M Mofizar Rahman.