There are at least five artists with the same name:
1 - Cockroach is a pseudonym for Dan Penta, a New York City based songwriter frequently associated with the Antifolk scene. This Cockroach has performed and recorded as a solo artist, as well as with his bands Hearth and Whisper Doll, and sometimes appears as a guest on others' records, like Kimya Dawson's "Hidden Vagenda."
Cockroach is also the name of:
2 - a black/death metal band from Germany.