He is always referred to with the article "the" suggesting that "Finn" is not a personal name, as if he is a Finn (from Finland, a Finnish person). However nothing in his description or backstory connects him to Finland.
The Finn is an antisocial man, and his personality seems to degrade over time, becoming less friendly in each appearance. He always lives alone, and is described as having agoraphobia in environments like Istanbul, and feeling more comfortable in crowded and enclosed spaces.
His closest friendship seems to be with Molly, who he often calls "Sweet Meat" (It is highly doubtful that any other business associate could get away with calling her this) with whom they can communicate discreetly with some sort of sign language. Despite his aloofness, the Finn still manages to keep up with news about where his former friends and associates have been (for example, informing Molly years after "Neuromancer" that Case is now married with four children). His age is never given, but he is implied to be quite old; on two separate occasions he has told someone, "I have a pair of shoes older than you" ("Burning Chrome" and "Count Zero"). His knees crack when he stands up.
The Finn is described as if he is genetically engineered for high-speed burrowing. He has a narrow, streamlined head and very small ears almost flat against his head. His teeth are yellow, with large front teeth canted sharply backward. He smokes Cuban Partagas and his fingers are smoke-stained.
He is seen wearing an old, tattered tweed jacket, which is so wide that floats across his shoulders and doesn't settle into position. He is armed with a kind of handgun when receiving visitors.
In Istanbul he was wearing a sarariman black suit, described by Molly as "rat in a business suit". His black silk tie was soon starting to resemble a worn carbon ribbon, and his lapels were soon stained by kebab gravy and fried eggs. Generally he is clumsy and unkempt and whatever he wears starts to get dirty and wear-out soon. Sometime he unsuccessfully tries to shake off dust or crumples.
He is a software fence who trafficks a variety of debugging and sensor gear. He also trades in stolen goods, without even knowing what they are. Coming into contact with other fences, sometimes he deals with more "traditional" precious items like metals, stamps, rare coins, gems, jewelry, furs and artworks.
It seems that he has some past friendship and history with Automatic Jack ("for the sake of old times"), as well as Molly Millions and in his appearances he aids them. He used to be annoyed by the sound of the servos of Jack's mechanical arm, which Jack knew and did to annoy him.
At some unspecified past time, he did business with Smith, an "art dealer". Knowing that the Finn has connections with the Memory Lane, he asked to hire a console cowboy to make an untraceable search on Tessier-Ashpoole. Finn demanded an explanation, and Smith told him everything about the precious talking head and a ninja assassin (possibly Hideo). The Finn hired a hacker (taking a percentage for his mediaton); they found that the coporation was in litigation and got the law firm. Through the lawyer's ICE they found the address, owning almost all Freeside station. The cowboy combined a precis for them. Seeing their fantastic tangle of powers of attorneys, Smith backed out, but the Finn remained in the story.
At some other time he was in Maryland where he had seen a horse, 3 years after the pandemic, shortly before their extinction.
Some muggers from New Jersey robbed someone and brought to the Finn a fake belgian passport and credit cards, which he burned, a Porsche watch and a cartridge. Next week Jack visited him to see what was available in hot software. He tried to sell him a Smith & Wesson 408 Tactical. To show his disinterest Jack drummed his mechanical fingers on the table, and the sound of the servos annoyed him; he jokingly tells him to pawn it and get something quieter. Then he offers him the mysterious cartridge for a bargain price, and Jack recognizes it as Russian, joking that it'd be as useful as sewage controls of Leningrad. The Finn tells him that doesn't sell the keys to the Kremlin; he expects from him to have more class and figure out what it himself, convincing him to buy it.
Sometime later Jack visits him again, as he had spent a lot of money looking for a money laundrey and went to buy a new blackbox rig. The Finn told him about the Long Hum family of stockbrokers in Macao.
Molly Millions proposed to Armitage to hire him as a tech for their job. However without Armitage's knowledge, Molly Millions and Case visited him in MH. The Finn led them to the secret room beyond Metro and did a scan for implants but didn't find anything. He was hired to fit Molly for a SimStim broadcast rig. Later he visited their loft in an abandoned building. Recognised by the security package, Case let him enter; after complaining for being too dark, they pretended to meet for a first time. The Finn produced a black rectangle, a flip flop switch, to wire it into his Ono-Sendai Cyberspace VII in order to access live Molly's sensorium.
His black aide brought Case and Molly to his secret room, while eating pickled herring and flatbread. Molly gestured silently and provided him a paper. He left, returned, secured the circuit door, and took a flat little concole. He said to Molly triumphantly that he tracked the origins of the Wintermute A.I., revealed to her by Lupus Yonderboy, and possibly it is backing their boss. He told them the story of Smith to explain to them the power of T-A.
Armitage later arranges the Finn to fetch their equipment from the loft to Istanbul. He was waiting for the pair sourly in the lobby of Istanbul Hilton wearing a new Shinjuku businessman suit, sarariman black, pointing out he wasn't paid enough to wear it, expressing his longing for Brooklyn. He handed them a magnetic key with a round yellow tag to to and meet their boss. He said he was there to check someone's implants, who Molly understood (showing a flicker of jive) was Peter Riviera.
The next day Terzibashjian led them to the Spice Bazaar, where he at least felt comfortable in the crowded and enclosed environment and was excited when he saw an embalmed horse; they stalked Riviera as he exited into an alley. When shooting started, he jerked Case down into a crouch. With the help of Mahmud they took Riviera away and scanned his gadgets while still unconscious. After his task the Finn returned home.
As a construct
Later in the book, Wintermute uses the Finn's personality to communicate with Case and Molly in the Matrix (as Wintermute chooses its appearance based on its subjects' memories).
Preparing for the run to Villa Straylight, Wintermute brought Case to a simulation of Metro Holografix and the SimStim ghost of the Finn appeared, smoking Partagas. He explained to him the nature of the simulation, how he accesses his memories, and how human memory is like a hologram. He revealed that he gave him that dream-memory with the hive.
The Finn returns in "Count Zero," more cynical, unfriendly, and threatening than ever before. Here, he proves that he is capable of defending himself, killing three would-be assassins with his "dog food trick." Though he helps the main characters (Lucas and Bobby) once again, he expresses none of the friendship that he showed to Bobby Quine, Automatic Jack, Molly or Case, instead regarding them with contempt and suspicion.
Mona Lisa Overdrive
By the events of "Mona Lisa Overdrive," the Finn has passed away. (The cause of death is not given, but since he is described as being very old even in "Burning Chrome," it is likely that he simply died of old age.) The Finn's old shop is now ruled by an A.I. construct based on his personality, created by the Finn himself before his death. His reason for doing this is never revealed. (It is plausible that he was inspired to do so after learning that Wintermute used his identity; but since it's never stated whether the Finn did in fact learn of that, it cannot be confirmed.)