I believe the person you are referring to is called "Nicky Eyes" in GoodFellas.

As Turnbull said, you can find not-so-detailed information about Paul Vario (Paulie Cicero), Jimmy Burke (Jimmy Conway), Tommy DeSimone (Tommy DeVito) and Henry Hill on Google.com, but from my basic knowledge on the Vario crew is that Paul Vario was Caporegime under Tommy Lucchese, who was Boss of the Lucchese Family during the early 1950s. Paul Vario's reign as Caporegime continued after Tommy's death, where he was Caporegime under Carmine Trumunti during the 1960s and then Tony Corallo during the 1970s and 80s, until his incarcaration and then his death in 1988. Al D'Arco succeeded Paul as Caporegime of the his former crew after his death.

I could only find one picture of Paul Vario, which I have posted below.