The Finn is a fence for stolen merchandise that runs his shop in the Sprawl. He's hired by Armitage to provide extra tech for Case's hacking console, and he travels with the group to Istanbul to validate Riviera's modifications. Later in the book, Wintermute uses the Finn's appearance to communicate with Case.
Although hired by Armitage, the Finn's first loyalties seem to be to his friend Molly as he lets Molly use his shop to make plans to spy on Armitage. Of course, she has to pay him for the privilege. Hey, they may be friends, but the Finn's still a professional.