caricature This is not a parody, but a friendly caricature.
impersonation I was doing an impersonation of my boss when he showed up.
mimicry How do I know your ability to speak isn't just an advanced form of mimicry?
ersatz They didn't have real coffee, so they drank ersatz.
copying They will not sanction copying without permission.
likeness A painter could not better describe his likeness.

Popularity over time

Use in printed books, per decade from 1850 to 2019.

By length

4 letters: copy², echo², mock¹, sham¹
5 letters: farce¹
6 letters: parody³, ersatz²
7 letters: copying³, replica³, mocking², mockery³, mimicry³, lampoon², mimesis
8 letters: likeness², travesty³, pretense², pretence
9 letters: duplicate³, burlesque², facsimile⁴, pasticcio
10 letters: simulation⁴, caricature⁴
11 letters: resemblance³, counterfeit³, replication⁴, epigonality
12 letters: reproduction⁴
13 letters: impersonation⁵

The small number after each word is its number of syllables (copy² = 2 syllables).