Someone who copies a well-known poet, closely imitating her style, is an epigone. You are also an epigone if you admire and imitate another kind of writer, a visual artist, or a musician.
If you put a lot of time into trying to duplicate the sound of your favorite rock star, recording covers of his hits or writing songs that sound almost identical to his, you're an epigone. You can also use the word to describe the follower of a particular philosopher, or an admirer of a famous chef, especially if you imitate her cooking style. Epigone has a Greek root, epigonos, "offspring or successor."