Sure, he may be a hit man, but where did his nickname come from?

Internet Source 1. 
... Anthony "Tony Roach" Rampino, whose physical features led to his nickname...

Internet Source 2.
He was never inducted into the Mafia because of his heavy drug use. He reportedly earned the nickname 'The Roach' because he smoked every bit of a marijuana joint.

Frish says:
A confederate of John Gotti's, Tony "The Roach" has served 10 years for for selling a Kilo of Heroin to an undercover cop, and may gain his freedom if the Judge decides he can go with time served.  He's never been indicted for several suspected killings.

I believe source two as to his nickname but cannot confirm.